Physics quiz question: object inside converging lens focal point

Physics 205B Quiz 2, spring semester 2020
Cuesta College, San Luis Obispo, CA

An object 1.0 cm in height is placed 16 cm in front of a converging lens with a focal length of +25 cm. The resulting image is:
(A) upright, diminished.
(B) upright, enlarged.
(C) inverted, diminished.
(D) inverted, enlarged.
(E) (No image would be produced.)

Correct answer (highlight to unhide): (B)

Solving for the location of the image d_i:

(1/d_o) + (1/d_i) = (1/f),

(1/d_i) = (1/f) – (1/d_o),

(1/d_i) = (1/(+25 cm)) – (1/(+16 cm)) = –0.0225 cm^–1,

d_i = 1/(–0.0225 cm^–1) = –44.444... cm,

where the negative sign by convention makes this a virtual image located to the right side of the lens (the side of the lens opposite the original object). The linear magnification m is given by:

m = h_i/h_o = –d_i/d_o = –(–44.444... cm)/(16 cm) = +2.777...,

which means that this virtual image is upright, due to the positive sign, and is enlarged, being about 2.8 times the size of the original object.

Sections 30882, 30883
Exam code: quiz02B3rD
(A) : 1 student
(B) : 21 students
(C) : 3 students
(D) : 10 students
(E) : 0 students

Success level: 60%
Discrimination index (Aubrecht & Aubrecht, 1983): 0.83

Online reading assignment: optical instruments

Physics 205B, spring semester 2020
Cuesta College, San Luis Obispo, CA

Students have a bi-weekly online reading assignment (hosted by SurveyMonkey.com), where they answer questions based on reading their textbook, material covered in previous lectures, opinion questions, and/or asking (anonymous) questions or making (anonymous) comments. Full credit is given for completing the online reading assignment before next week's lecture, regardless if whether their answers are correct/incorrect. Selected results/questions/comments are addressed by the instructor at the start of the following lecture.

The following questions were asked on reading textbook chapters and previewing presentations on optical instruments and interference.


Selected/edited responses are given below.

Describe what you understand from the assigned textbook reading or presentation preview. Your description (2-3 sentences) should specifically demonstrate your level of understanding.

"Magnifiers make objects appear bigger than they are by increasing the angular size of an object. An object that is farther away appears smaller because the angular size is smaller."

"From this section I learned that telescopes and microscopes have a different set of lenses in order to either magnify an object that is small or an object that is far away. The different lenses in both of the instruments allow each to provide different functions."

"Ray tracings for both microscopes and telescopes create real intermediate images because the rays actually converge. I am beginning to understand that placing the object just outside the focal point of the objective will result in an enlarged image."

"Microscopes use two converging lenses to zoom in on objects that are very small. The first lens, or the objective, creates a real, enlarged image in front of the second lens. This image is then used as the object for the eyepiece, which translates to an upright, virtual view of the original object."

"During microscope magnification, the focal length of the objective lens is decreased and the focal length of the eyepiece is also decreased. Conversely, in telescope magnification, the focal length of the objective lens is increased while the focal length of the eyepiece lens in decreased."

"I understand how a microscope works before reading the text since I had to understand it for biology but now I did learn about the equation for it. I didn't know that it even had an equation before so it was interesting to learn."

"The objective makes an image just inside the eyepiece focal length. The eyepiece projects this first image to an infinite distance so a relaxed eye can see the final image."

"In a compound microscope or telescope, the angular magnification is the angular size of the final image divided by the reference angular size. A difference between them is that the image in a telescope is first diminished before being magnified while a compound microscope enlarges twice."

"I now understand how a compound microscope is designed to work, something I have never thought about before in all of my years of using them in school. They work by having an additional converging lens (objective) 'pre-magnify' the image before it passes through the magnifying glass (eyepiece), ultimately increasing the angular magnification."

"I understand the microscope parts because of taking biology. I understand that the 'tube length' for microscopes is defined as the distance measured between the objective and eyepiece focal points. the 'barrel length' for telescopes is defined as the distance measured between the objective to the eyepiece lenses, which is the same as the sum of their focal points."

"Microscopes and telescopes have some similarities such as the placement of an objective at the front leading to an eyepiece in the back. Moreover, both instruments create the same ray tracing. The main difference between these two instruments is the location of the physical object. For example, the object for a microscope is located just outside of the focal point of the objective while the telescope showcases an object extremely far away."

"There is a negative sign in both the microscope and telescope magnification equations. The negative sign for both denotes that the image produced will be inverted."

Describe what you found confusing from the assigned textbook reading or presentation preview. Your description (2-3 sentences) should specifically identify the concept(s) that you do not understand.

"I don't quite know why but memorizing the ray tracings is still a little difficult."

"I would like a little more information on these ray tracings and how to memorize the differences from the ones we've previously done."

"I do not understand how to draw a telescope ray tracing. I also do not understand why when talking about magnification, that only focal distance is taken into consideration."

"I found confusing the formulas used to calculate the magnifications. Each formula was different depending on the optical instrument."

"I do not fully understand the ray tracings behind the microscope and telescope concepts. I am also unsure how to utilize the equations."

"I would like to go over the angular magnification equations in class. I am a little bit confused about why the magnification factors are negative, primarily."

"I'm not really confused on anything because there wasn't much in the reading, which is what usually confuses me but telescope and microscope are similar. The equations are also distinct enough not to get them confused."

"I believe I understood this topic."

Identify the type for each of these lenses. (Only correct responses shown.)

Microscope objective: converging [94%]
Microscope eyepiece: converging [71%]
Telescope objective: converging [79%]
Telescope eyepiece: converging [59%]

Identify the ray tracing for each of these lenses. (Only correct responses shown.)

Microscope objective: ray tracing 2 [74%]
Microscope eyepiece: ray tracing 3 (or 4) [44%]
Telescope objective: ray tracing 3 (reversed) [0%]
Telescope eyepiece: ray tracing 3 (or 4) [44%]

A (compound) microscope should have a __________ focal length objective lens and a ___________ focal length eyepiece lens in order to maximize its angular magnification.

short; short.	*************** [15]
short; long.	************** [14]
long; short.	* [1]
long; long.	[0]
(Unsure/lost/guessing/help!)	**** [4]

A telescope should have a __________ focal length objective lens and a ___________ focal length eyepiece lens in order to maximize its angular magnification.

short; short.	[0]
short; long.	** [2]
long; short.	********************** [22]
long; long.	****** [6]
(Unsure/lost/guessing/help!)	**** [4]

Ask the instructor an anonymous question, or make a comment. Selected questions/comments may be discussed in class.

"A little extra help with these two-part ray tracings would be awesome!"

"Please explain the initial and final images produced by a microscope."

"May we review how to compare real-life examples to ray tracings?"

"Can we review how to actually use the equations for the magnification of the microscope and telescope please?"

"Cool concepts, but a tad difficult."

"Why are we learning about microscopes and telescopes?" (We're just finishing up the optics section of this course with some cool stuff.)

"Why can't we use the same angular magnification formula for both the microscope and telescope?" (Even though both the microscope and telescope use an eyepiece the same way (to magnify the images made but the objective lenses), the objective lens for a microscope looks at an object very close to it, just outside its focal point, while the objective lens for a telescope looks at an object very far away, essentially out at infinity. So the differences between the microscope and telescope equations object distances primarily result from the different uses of the objective lenses.)

"When looking at the ray tracing, the ray tracing to the eyepiece looks like converging lens tracing #3. However, the rays never intersect on this ray tracing. How is this possible?" (Your relaxed eye is set to look at things infinitely far away. The rays from an object at infinity are parallel as they hit your eye. So an eyepiece will take an object at its focal point and its rays will be parallel (which would normally not produce an image), but your eye will take those parallel rays as something it thinks is infinitely far away, and easily focus those rays to interpret it as being from a distant location (but apparently with a very large angular size.)

Online reading assignment: corrective optics, magnifiers

Physics 205B, spring semester 2020
Cuesta College, San Luis Obispo, CA

Students have a bi-weekly online reading assignment (hosted by SurveyMonkey.com), where they answer questions based on reading their textbook, material covered in previous lectures, opinion questions, and/or asking (anonymous) questions or making (anonymous) comments. Full credit is given for completing the online reading assignment before next week's lecture, regardless if whether their answers are correct/incorrect. Selected results/questions/comments are addressed by the instructor at the start of the following lecture.

The following questions were asked on reading textbook chapters and previewing presentations on corrective optics and magnifiers.


Selected/edited responses are given below.

Describe what you understand from the assigned textbook reading or presentation preview. Your description (2-3 sentences) should specifically demonstrate your level of understanding.

"I understood the presentation on myopia. I think it was super cool to see how we are entry-level optometrists after this."

"Refractive power is used by optometrists to measure the degree at which light is converged or diverged denoted by a (+) or (–) sign. It is also the inverse of the focal length."

"The combined total refractive power for two lenses is addition of each refractive power."

"Negative values for the focal length and refractive power mean that corrective lenses should be diverging, to correct for the person's myopia. Corrective lenses with a positive focal length and refractive power will be converging lenses, to correct for hyperopia."

"Magnifiers 'magnify' by increasing the angular size of the object thus making the object appear bigger to the eye. Increasing the distance between the object and the eye provides a smaller angular size and makes the object appear smaller."

"Angular size is the size of an object at a certain distance. The larger the object, the larger the angular size. Magnification isn't really magnifying but rather the lens allows the eye to be able to focus on the object at a distance where it other wise wouldn't have been able to."

Describe what you found confusing from the assigned textbook reading or presentation preview. Your description (2-3 sentences) should specifically identify the concept(s) that you do not understand.

"Corrective optics. It all seems overwhelming, but simplification will help. Especially refractive power and power addition equations."

"Still figuring out how to work with the thin-lens equations. The steps for correcting myopia and hyperopia were a little confusing."

"I am a little confused on the important difference(s) between linear and angular magnification. I think that I get the basic idea of both but want to make sure I clearly understand how they differ."

"Maybe a little more clarification on the mathematics on angular magnification."

"I did not understand how the eye can perceive the penny to be bigger than the moon. I also did not understand the idea of doing multiple thin lens equations for two lens."

"A review of the equations for angular size and angular magnification would be very helpful. Also I am not really sure about what it exactly means when 'the image is at infinity.'"

"The math seems a little confusing to me right now per usual. But it's late and I'm sleepy."

In general, a converging lens will produce virtual, upright images located __________ the original object.

closer than.	******* [7]
at the same distance as.	** [2]
farther than.	********************** [22]
(Unsure/lost/guessing/help!)	* [1]

In general, a diverging lens will produce virtual, upright images located __________ the original object.

closer than.	************************** [26]
at the same distance as.	[0]
farther than.	***** [5]
(Unsure/lost/guessing/help!)	* [1]

Identify the type of lens used for these optics. (Only correct responses shown.)

Glasses/contacts to correct for myopia: diverging [75%]
Glasses/contacts to correct for hyperopia: converging [78%]
Glasses/contacts to correct for presbyopia: converging [29%]
Magnifying lenses: converging [74%]

State the units of refractive power for lenses, and briefly describe the relationship between refractive power P and focal length f.

"Diopters. Refractive power is 1/f."

"The unit of refractive power for lenses is diopters, which is the inverse of the focal length."

"Units for P are meters^–1."

"I don't understand what this is asking. "

Explain the difference between the two types of magnification, m and M.

"Linear magnification is 'm' and angular magnification is 'M.'"

"m is the ratio of the object's distance or height to the images distance or height at convergence of the light rays h_i/h_o or –d_i/d_o. M is how much the apparent size of something is change by a magnifying lens. The apparent size is an illusion and relative to the viewer."

"m is the ratio of image height to object height while M is a distinct ratio of angular size of some image produced by an optical instrument divided by the reference angular size of an object viewed without an optical instrument."

"I'm not sure what the answer is."

"Again, I am pretty lost."

"Don't remember."

A nominal, relaxed eye is set to focus on objects located at:

+∞.	************ [12]
+25 cm (at your near point).	*********** [11]
+f (at the focal point of the lens).	**** [4]
(Unsure/lost/guessing/help!)	***** [5]

If an object is brought closer to your eye, its angular size will:

increase.	**************************** [28]
decrease.	* [1]
remain unchanged.	[0]
(Unsure/lost/guessing/help!)	*** [3]

When a converging lens is used as a simple magnifier, the object is placed at a distance d_o = __________ in front of (to the left of) the lens.

+∞.	**** [4]
+25 cm (at your near point).	************* [13]
+f (at the focal point of the lens).	********** [10]
(Unsure/lost/guessing/help!)	***** [5]

The ray tracing that best matches when a converging lens is used as a simple magnifier is:

#3.	* [1]
#4.	*************************** [27]
(Unsure/lost/guessing/help!)	**** [4]

Ask the instructor an anonymous question, or make a comment. Selected questions/comments may be discussed in class.

"Can you show a drawing demonstrating the difference between microscope and telescope lens placement and rays? I was confused with presbyopia and how that age-onset disorder works with myopia. (1) In that case someone would be unable to see far--myopia--while simultaneously being unable to see close--presbyopia? Also (2) can someone experience hyperopia and presbyopia or would the condition default to the latter? Finally, while partially off-topic, (3) is there a physics-based description of blindness?" ((1) Yes, someone with myopia (can see near, can't see far) who develops presbyopia (can't see near) would then require bifocals to correct both problems. (2) If you can't see near as a child, you have congenital hyperopia. If you could see near when you were young, but gradually lost that ability as you got older, then you have presbyopia, which is basically age-onset hyperopia, and they are both corrected with a (stronger) converging lens prescription. (3) Not really, I would think that's more of a biology/anatomy/physiology thing.)

"Can we go over problems or see these problems done? When I see these equations being used it makes it easier to understand."

"I have some questions about what a relaxed eye is meant to focus on."

"Please help to understand the angular size and tie all the equations to the ray tracing, this is getting complex."

"I'm not too confident on my answer for how close a simple converging lens used as a magnifier should be."

"I would love more examples of how to guess what kind of ray tracing would apply to real-life situations like a magnifier."

"I think angular magnification is the hardest part of this section, especially when comparing them to ray tracings." (It really is. More on angular magnification next week.)

"Can the human eye control the amount of light that comes in?" (It make less light come in (by making the pupil smaller, or by squinting your eyelids), but it can't make more light coming in than is already there.)

"Do you meditate? Moreover, if you do meditate, do you call it 'total internal reflection?' (Sorry I'm a couple chapters late on this joke.)" (I think my meditation chill is more like something called 'frustrated total internal reflection.' It's when total internal reflection is supposed to happen, but introducing an external object with a new index of refraction that barely touches that surface ruins the total internal reflection, allowing a transmitted ray to go through.)

"How long have you taught physics?" (My first physics class as an instructor was at UC-Davis 26 years ago, when I was still a graduate student.)

Online reading assignment: images produced by lenses, thin lens equations, cameras and eyes

Physics 205B, spring semester 2020
Cuesta College, San Luis Obispo, CA

Students have a bi-weekly online reading assignment (hosted by SurveyMonkey.com), where they answer questions based on reading their textbook, material covered in previous lectures, opinion questions, and/or asking (anonymous) questions or making (anonymous) comments. Full credit is given for completing the online reading assignment before next week's lecture, regardless if whether their answers are correct/incorrect. Selected results/questions/comments are addressed by the instructor at the start of the following lecture.

The following questions were asked on reading textbook chapters and previewing presentations on examples of images produced by lenses, thin lens equations and camera and eyes.


Selected/edited responses are given below.

Describe what you understand from the assigned textbook reading or presentation preview. Your description (2-3 sentences) should specifically demonstrate your level of understanding.

"Converging lenses cause light rays to converge toward a focal point, while diverging lenses cause light to diverge (spread out). Converging lenses can produce either real or virtual images, while diverging lenses can only produce virtual images. The thin lens and magnification equations help us determine the location, size, and nature of the image a lens produces."

"I understand the image tracings a little bit better. I understand how the height and what side of object the image is on effects the the orientation and size of the image. I also understand that if the lines can be traced back that makes the image virtual."

"When drawing ray tracings, rays move from left-to-right with the object located on the left of the lens. Once the tracing is complete, if it is a virtual image, then the image would be located on the left of the lens. If the image is real then the image will be located to the right of the lens."

"The magnification equation uses the ratio of image height to object height, or the negative value of image distance to object distance. Regardless of whether or not the image is enlarged or diminished, an upright image will always have a positive height value and an inverted image will have a negative height value."

"How the thin lens equation and magnification equation are derived. I understand the basics of the thin-lens and magnification formula. I understand how near point is corrected for someone who is farsighted and how the far point is corrected using a diverging lens for someone who is nearsighted."

"This section is still on converging and diverging lens, however, it talks about how cameras and eyes are similar because they are both converging lens which produce real images. Camera have a fixed focal length lens meaning on the image and object distance is the only thing influencing its equation. Eyes have fixed image length distance since the eye is constant. This means that only object distance and focal lens are then only factors that can change."

"The difference in the different 'sighted-nesses.' Myopia being nearsighted, meaning they can see things near to them better. Versus hyperopia being far-sighted meaning they can see things far to them better. I have heard of these terms before, but it is cool to know the physics behind it!"

Describe what you found confusing from the assigned textbook reading or presentation preview. Your description (2-3 sentences) should specifically identify the concept(s) that you do not understand.

"Real and virtual images are still giving me a little but of trouble. I am always unsure on my answers. Also comparing ray tracings was oddly difficult."

"I'm still struggling to understand how to distinguish between real/virtual, upright/inverted, and enlarged/diminished images."

"I'm still confused about what kind of image is produced through each lens, whether the image is real, virtual. I'm also not sure how to apply the thin lens equation."

"I'm still having trouble with the distinction of real image versus virtual image. Diverging lens are always virtual I believe but need more refreshing of these concepts."

"I do not understand the sign conventions for lenses, drawing ray tracings might help. The sign conventions were just given as a list in the book so it's hard to relate them to images being formed."

"How to use the thin lens and magnification equations correctly in-relation to examples. Need some example problems and discussion to process this quantitatively to the best of my ability."

Identify the following thin lens parameters. (Only correct responses shown.)

Focal length: f [91%]
(Linear) magnification factor: m [89%]
Object distance: d_o [94%]
Object height: h_o [83%]
Image distance: d_i [86%]
Image height: h_i [94%]

For a simple camera, identify which parameter(s) must change or remain constant in order to focus on different distance objects.

Focal length: remains constant [49%]
Lens-to-film distance: changes [60%]

For a model eye, identify which parameter(s) must change or remain constant in order to focus on different distance objects.

Focal length: changes [80%]
Lens-to-retina distance: remains constant [74%]

Identify the type of lens, image, and example ray tracing produced in the online reading assignment examples. (Only correct responses shown.)

Lens: converging [66%] (Only converging lenses can make inverted images.)
Image: real [63%] (All inverted images are real.)
Ray tracing: 1 [46%]

Lens: diverging [43%] (Only diverging lenses can make upright, diminished images.)
Image: virtual [46%] (All upright images are virtual.)
Ray tracing: 6 [26%]

Lens: converging [60%] (Only converging lenses can make upright, enlarged images.)
Image: virtual [46%] (All upright images are virtual.)
Ray tracing: 4 [20%]

Lens: diverging [49%] (Only diverging lenses can make upright, diminished images.)
Image: virtual [49%] (All upright images are virtual.)
Ray tracing: 7, 8, 9 or 10 [31%]

Lens: converging [40%] (Only converging lenses can make inverted images.)
Image: real [40%] (All inverted images are real, as the candle is upright, and the projected image is upside-down.)
Ray tracing: 1 [11%]

Lens: diverging [51%] (Only diverging lenses can make upright, diminished images.)
Image: virtual [54%] (All upright images are virtual.)
Ray tracing: 7, 8, 9 or 10 [28%]

Lens: converging [60%] (Only converging lenses can make upright, enlarged images.)
Image: virtual [46%] (All upright images are virtual.)
Ray tracing: 5 [29%]

Lens: converging [54%] (Only converging lenses can make inverted images.)
Image: real [46%] (All inverted images are real, as the slide is upside-down, making the projected image on the wall upright.)
Ray tracing: 2 [26%]

A person with no vision defects can see both nearby and distance objects. Identify what can be seen by a person with the following vision defects. (Only correct responses shown.)

Myopia: can see nearby objects [97%]
Hyperopia: can see distant objects [97%]
Presbyopia: can see distant objects [91%]

Ask the instructor an anonymous question, or make a comment. Selected questions/comments may be discussed in class.

"Can we please go over real and virtual images again in the examples above? I wasn't sure how to identify the ray tracings."

"I really just don't understand how we can tell whether an image is produced from a converging or diverging lens. So confused!"

"I feel that I need a lot of help with the lenses and real-life examples because I feel lost."

"Is the difference between concave and convex lenses the same as the difference between converging and diverging lenses?" (Yes, exactly.)

"I'm really unsure of how to distinguish between what produces a real or virtual image just based on the object. I feel like I missed a blog presentation that explained this because I've looked through them and I can't seem to find the best resource to help me understand them. I can see on the worksheet where the light rays intersect (or don't) if they are real or virtual and also if they are upright or diminished. I just don't know how we can determine this just be knowing what object light isis passing through. Maybe I am missing something really obvious?" (We officially didn't have a super-specific reading or lecture on this, but we had a flowchart to determine whether an image or real or virtual, and this process is something we'll pick up from practice rather than from strict formal definitions.)

"I thought this chapter was very intriguing because of its relation to human anatomy."

"Is it accurate to say that you can see a real image without having to look directly through a converging lens but in order to see a virtual image you have to look through the lens that produced it?" (Yes. You can only project a real image onto a screen, as you'll be doing in lab this week. You can see both real or virtual images by looking back through the lens.)

"Interesting material, also it's just been so cold in the mornings lately!"

Physics midterm question: comparing diverging lens image sizes

Physics 205B Midterm 1, spring semester 2019
Cuesta College, San Luis Obispo, CA

An object 1.0 cm in height is placed 16.0 cm in front of a f = –15.0 cm diverging lens, producing an image. Show that moving the object slightly closer, such that it is 14.0 cm in front of this diverging lens will result in a slightly larger image than before. Explain your reasoning by using ray tracings and/or thin lens equations, properties of lenses, images, and magnification.

Solution and grading rubric:

• p:
  Correct. Proves that the object should be as close to the diverging lens as possible in order to obtain the largest image (largest linear magnification factor) using either of these two methods:
  1. calculating the image distances produced by the different object distances, and finds the resulting respective image sizes and/or linear magnification factors; or
  2. drawing two carefully, properly scaled ray tracing diagrams.
• r:
  As (p), but argument indirectly, weakly, or only by definition supports the statement to be proven, or has minor inconsistencies or loopholes. May have misplaced values, but consistently interprets resulting numbers.
• t:
  Nearly correct, but argument has conceptual errors, or is incomplete. Problematic algebra (combines fractions by combining denominators, forgets to invert (1/f – 1/d_o) to solve for d_i, etc.).
• v:
  Limited relevant discussion of supporting evidence of at least some merit, but in an inconsistent or unclear manner. Some garbled attempt at applying properties of lenses, images, and linear magnification. Typically has problematic algebra as in (t), but does not use (erroneous) d_i values to find image heights or linear magnification factors for comparison.
• x:
  Implementation/application of ideas, but credit given for effort rather than merit. No clear attempt at applying properties of lenses, images, and angular magnification.
• y:
  Irrelevant discussion/effectively blank.
• z:
  Blank.
  

Grading distribution:
Sections 30882, 30883
Exam code: midterm01Ft6G
p: 25 students
r: 6 students
t: 4 students
v: 4 students
x: 2 students
y: 0 students
z: 0 students

A sample "p" response (from student 1810), using two sets of thin lens equations:
Another sample "p" response (from student 0691), using two ray tracings:

Physics quiz question: focal length of a diverging lens

Physics 205B Quiz 2, spring semester 2019
Cuesta College, San Luis Obispo, CA

An object 1.0 cm in height located 8.0 cm in front of a diverging lens produces an upright image that is 0.75 cm in height. The focal length of this diverging lens is:
(A) –24 cm.
(B) –11 cm.
(C) –6.0 cm.
(D) –3.4 cm.

Correct answer (highlight to unhide): (A)

From the linear magnification equation:

m = h_i/h_o = –d_i/d_o,

the ratio between the image distance d_i and object distance d_o (8.0 cm) can be determined from the given image height h_i (+0.75 cm) and object height h_o (1.0 cm):

h_i/h_o = –d_i/d_o,

(+0.75 cm)/(1.0 cm) = –d_i/(8.0 cm),

–(8.0 cm)·(+0.75 cm)/(1.0 cm) = d_i = –6.0 cm.

Substituting this result for d_i into the thin lens equation will then obtain a value for the focal length f, as the object distance d_o is given:

(1/d_o) + (1/d_i) = (1/f),

(1/(8.0 cm)) + (1/(–6.0 cm)) = (1/f),

–0.04166666667... cm^–1 = (1/f),

–24 cm = f,

which is negative, as expected for a diverging lens.

(Response (B) is d_o·h_o/h_i; response (C) is d_i; response (D) is d_i·d_o/(d_o – d_i).)

Sections 30882, 30883
Exam code: quiz02BTLn
(A) : 17 students
(B) : 4 students
(C) : 7 students
(D) : 13 students

Success level: 41%
Discrimination index (Aubrecht & Aubrecht, 1983): 0.90

Physics quiz question: object just outside converging lens focal point

Physics 205B Quiz 2, spring semester 2019
Cuesta College, San Luis Obispo, CA

A converging lens has a focal length of +10.0 cm. An object 0.50 cm in height is placed at a distance of 12.5 cm in front of the lens, which will produce a(n) __________ image.
(A) diminished, real.
(B) enlarged, real.
(C) diminished, virtual.
(D) enlarged, virtual.
(E) (No image would be produced.)

Correct answer (highlight to unhide): (B)

Solving for the location of the image d_i:

(1/d_o) + (1/d_i) = (1/f),

(1/d_i) = (1/f) – (1/d_o),

(1/d_i) = (1/(+10.0 cm)) – (1/(+12.5 cm)) = +0.0200 cm^–1,

d_i = 1/(0.02 cm^–1) = +50.0 cm,

where the positive sign by convention makes this a real image located to the right side of the lens (the side of the lens opposite the original object). The linear magnification m is given by:

m = h_i/h_o = –d_i/d_o = –(+50.0 cm)/(12.5 cm) = –4.00,

which means that this real image is enlarged, being four times the size of the original object (and will be inverted, due to the negative sign).

Sections 30882, 30883
Exam code: quiz02BTLn
(A) : 10 students
(B) : 23 students
(C) : 3 students
(D) : 4 students
(E) : 1 student

Success level: 56%
Discrimination index (Aubrecht & Aubrecht, 1983): 0.53

Online reading assignment: optical instruments

Physics 205B, spring semester 2019
Cuesta College, San Luis Obispo, CA

Students have a bi-weekly online reading assignment (hosted by SurveyMonkey.com), where they answer questions based on reading their textbook, material covered in previous lectures, opinion questions, and/or asking (anonymous) questions or making (anonymous) comments. Full credit is given for completing the online reading assignment before next week's lecture, regardless if whether their answers are correct/incorrect. Selected results/questions/comments are addressed by the instructor at the start of the following lecture.

The following questions were asked on reading textbook chapters and previewing presentations on optical instruments and interference.


Selected/edited responses are given below.

Describe what you understand from the assigned textbook reading or presentation preview. Your description (2-3 sentences) should specifically demonstrate your level of understanding.

"The objective lens is nearest to the object and the eyepiece (or magnifying glass) is nearest to the eye for both the microscope and telescope."

"For a two-lens model of a microscope and a telescope, the object uses light from the object to create a real image that will become the object for the eye piece. For a microscope, since the object is close to the focal point, the image produced is highly enlarged. On a telescope, however, the object is going to be very distant and the ray tracing becomes parallel before it is focused by the objective."

"The similarities between microscopes and telescopes: they both have tubes that hold two lenses apart from each other and have an objective lens in the front and an eyepiece in the back. The ray tracings are different, however."

"The first image/second object produced by the objective for both a microscope and telescope is near the focal point of the eyepiece. Because it is near the focal point of the eyepiece, the light transmitted through the eyepiece is nearly parallel. The final image produced is enlarged, virtual and near infinity."

"Both a microscope and telescope consists of an objective and an eyepiece. Angular magnification of a compound microscope: the M is greater when f_o and f_e are as short as possible and when the distance between lenses, L, is large. angular magnification for telescope: the objective should have a long focal length and the eyepiece a short focal length."

Describe what you found confusing from the assigned textbook reading or presentation preview. Your description (2-3 sentences) should specifically identify the concept(s) that you do not understand.

"I reviewed the lecture, but I still do not feel like I understand the difference between a microscope and telescope. I know the first object is a different distance from the objective and the image it creates is around the focal point of the eyepiece. But what are the lenses (or focal points?) doing differently?"

"I am not sure what type of focal lengths you would want for an objective lens for a microscope or telescope. I am not sure type of focal lengths I would want for the microscope and the telescope."

"The differences between the telescope and microscope magnification equations. Possibly it is due to the objects being placed at different focal lengths but I am not sure. To me it seems like both instruments essentially do the same thing so their magnification equations shouldn't be different."

"The ray tracings for the telescope and microscope. Also how the ray tracings for both are so similar."

"Why the formulas for the magnification equations of microscopes and telescopes differ."

"I'm a little confused because now we have two objects and two lenses involved in our ray tracings."

"When I read the readings I will know what I know, but I will also know what I do not know and that will go here."

"I really struggle with these sections and am not 100% sure what I'm confused on. Talking it out with examples in class always helps, but working on this section at home is a struggle for me."

"Nothing really too confusing."

Identify the type for each of these lenses. (Only correct responses shown.)

Microscope objective: converging [85%]
Microscope eyepiece: converging [64%]
Telescope objective: converging [85%]
Telescope eyepiece: converging [67%]

Identify the ray tracing for each of these lenses. (Only correct responses shown.)

Microscope objective: ray tracing 2 [46%]
Microscope eyepiece: ray tracing 3 (or 4) [41%]
Telescope objective: ray tracing 3 (reversed) [13%]
Telescope eyepiece: ray tracing 3 (or 4) [38%]

A (compound) microscope should have a __________ focal length objective lens and a ___________ focal length eyepiece lens in order to maximize its angular magnification.

short; short.	********************** [22]
short; long.	****** [6]
long; short.	*** [3]
long; long.	[0]
(Unsure/lost/guessing/help!)	******** [8]

A telescope should have a __________ focal length objective lens and a ___________ focal length eyepiece lens in order to maximize its angular magnification.

short; short.	* [1]
short; long.	*** [3]
long; short.	********************** [22]
long; long.	****** [6]
(Unsure/lost/guessing/help!)	******* [7]

Ask the instructor an anonymous question, or make a comment. Selected questions/comments may be discussed in class.

"Could you review a little more about the angular magnification in class? I am still struggling with that a little bit."

"No questions today but I am still a little confused on the magnification equations for both instruments."

"What does it mean when an image 'goes out into infinity?'"