Physics quiz archive: lenses, optical instruments

Physics 205B Quiz 2, spring semester 2019
Cuesta College, San Luis Obispo, CA
Sections 30882, 30883, version 1
Exam code: quiz02B3rD



Sections 30882, 30883 results

0- 6 :
7-12 :	*** [low = 7]
13-18 :	*****
19-24 :	********************* [mean = 21.5 +/- 5.2]
25-30 :	****** [high = 30]

Physics quiz archive: lenses, optical instruments

Physics 205B Quiz 2, spring semester 2019
Cuesta College, San Luis Obispo, CA
Sections 30882, 30883, version 1
Exam code: quiz02BTLn



Sections 30882, 30883 results

0- 6 :
7-12 :	*** [low = 9]
13-18 :	***************
19-24 :	************* [mean = 20.5 +/- 5.5]
25-30 :	********** [high = 29]

Physics midterm problem: diverging lens and converging lens

Physics 205B Midterm 1, spring semester 2018
Cuesta College, San Luis Obispo, CA

An object 1.0 cm in height is placed 5.0 cm in front of a f = –20.0 cm diverging lens, producing an upright image. This same 1.0 cm high object is then placed an unknown distance in front of a f = +20.0 cm converging lens, producing an inverted image that is the same size as the upright image originally produced by the diverging lens.

Determine (a) the size of the image produced by the diverging lens, and (b) the distance of this object in front of the f = +20.0 cm converging lens.

Show your work and explain your reasoning by using ray tracings and/or thin lens equations, properties of lenses, images, and magnification.

Solution and grading rubric:

• p:
  Correct. Identifies relevant parameters to methodically use the thin lens equation and linear magnification equation, in order to determine:
  1. that for the diverging lens, h_o = +1.0 cm, d_o = +5.0 cm, f = −20.0 cm, and uses thin lens equation to either find d_i = −4 cm (a virtual image) to find image height h_i = +0.8 cm (upright image) from the linear magnification equation, or may eliminate d_i in both equations to solve for h_i directly; and
  2. for the converging lens, h_o = +1.0 cm (the same object), d_o and d_i are both unknown, f = +20.0 cm, and h_i = −0.8 cm (inverted image that is the same size as the upright image produced by the diverging lens), and eliminates d_i in both equations to find d_o = +45 cm. May include very minor math errors with handling fractions and inverses.
• r:
  Nearly correct, but includes minor math conceptual errors, typically overlooking the fact that the image produced by the converging lens is inverted.
• t:
  Nearly correct, but approach has conceptual errors, and/or major/compounded math errors. At least solves for (1) successfully, and still attempts to methodically use this information in (2) to solve for the object distance for the converging lens. Typically makes multiple conceptual errors, such as overlooking the fact that the image produced by the converging lens is inverted; claiming that the image distance for the converging lens is the same as the image distance for the diverging lens, etc.
• v:
  Implementation of right ideas, but in an inconsistent, incomplete, or unorganized manner. Some garbled attempt at ray tracings and/or thin lens equations, the properties of lenses, images, and magnifications.
• x:
  Implementation of ideas, but credit given for effort rather than merit. No clear attempt at applying ray tracings and/or thin lens equations, the properties of lenses, images, and magnifications.
• y:
  Irrelevant discussion/effectively blank.
• z:
  Blank.
  

Grading distribution:
Sections 30882, 30883
Exam code: midterm01cVdP
p: 4 students
r: 7 students
t: 24 students
v: 0 students
x: 0 students
y: 0 students
z: 0 student

A sample "p" response (from student 7164):

Physics quiz archive: lenses, optical instruments

Physics 205B Quiz 2, spring semester 2018
Cuesta College, San Luis Obispo, CA
Sections 30882, 30883, version 1
Exam code: quiz02P0wR



Sections 30882, 30883 results

0- 6 :
7-12 :
13-18 :	************** [low = 14]
19-24 :	***************** [mean = 20.4 +/- 3.8]
25-30 :	*** [high = 30]

Physics midterm problem: extending telescope length

Physics 205B Midterm 1, spring semester 2017
Cuesta College, San Luis Obispo, CA

Two converging lenses, with focal lengths of +40.0 cm (for the objective lens) and +2.5 cm (for the eyepiece) are used to make a telescope. The length of the telescope (measured from lens-to-lens) is adjusted by sliding cardboard tubes in or out. Starting with the telescope used to look at an object very far away (essentially at infinity), determine how much the length must be extended in order to look at a closer object 10 m away. Show your work and explain your reasoning by using ray tracings and/or thin lens equations, properties of lenses, images, and magnification.


[*] Alan M. MacRobert, "Astronomy with a $5 Telescope," Sky & Telescope, vol. 79 no. 4 (April 1990), p. 384.

Solution and grading rubric:

• p:
  The eyepiece must be moved back by approximately 2 cm because:
  1. the object at d_o1 = +∞ for the objective creates a real image at d_i1 = f₁ = +40.0 cm, which becomes the object at a distance d_o2 = f₂ = +2.5 cm for the eyepiece, thus the telescope length (lens-to-lens distance) is 40.0 cm + 2.5 cm = 42.5 cm;
  2. the object at d_o1 = +10 m for the objective creates a real image at a slightly farther distance of d_i1 = +41.7 cm, which becomes the object at the same distance d_o2 = f2 = +2.5 cm for the eyepiece, thus the telescope length (lens-to-lens distance) is now slightly longer: 41.7 cm + 2.5 cm = 44.2 cm;
  3. thus the slight increase (approximately 2 cm) in the objective image distance d_i1 requires the eyepiece to be moved back by the same amount in order for this image to be placed at its front focal point.
• r:
  As (p), but argument indirectly, weakly, or only by definition supports the statement to be proven, or has minor inconsistencies or loopholes.
• t:
  Nearly correct, but approach has conceptual errors, and/or major/compounded math errors. At least understands that the telescope length is f₁ + f₂ when focused at ∞, and some attempt at finding the telescope length d_i1 + f₂ when focused at a finite d_o1.
• v:
  Limited relevant discussion of supporting evidence of at least some merit, but in an inconsistent or unclear manner. Some garbled attempt at ray tracings and/or thin lens equations, the properties of lenses, images, and magnifications. May have used microscope magnification equation to find length between lenses.
• x:
  Implementation/application of ideas, but credit given for effort rather than merit. No clear attempt at applying ray tracings and/or thin lens equations, the properties of lenses, images, and magnifications.
• y:
  Irrelevant discussion/effectively blank.
• z:
  Blank.
  

Grading distribution:
Sections 30882, 30883
Exam code: midterm01AhC4
p: 5 students
r: 0 students
t: 7 students
v: 17 students
x: 1 student
y: 0 students
z: 0 students

A sample "p" response (from student 1412):

Physics quiz archive: lenses, optical instruments

Physics 205B Quiz 2, spring semester 2017
Cuesta College, San Luis Obispo, CA
Sections 30882, 30883, version 1
Exam code: quiz02J4sZ



Sections 30882, 30883 results

0- 6 :
7-12 :	**** [low = 9]
13-18 :	********
19-24 :	********** [mean = 20.2 +/- 6.6]
25-30 :	******** [high = 30]

Physics quiz archive: lenses, optical instruments

Physics 205B Quiz 2, spring semester 2016
Cuesta College, San Luis Obispo, CA
Sections 30882, 30883, version 1
Exam code: quiz02f3MA


Sections 30882, 30883 results

0- 6 :
7-12 :	* [low = 11]
13-18 :	*******
19-24 :	********************* [mean = 23.0 +/- 4.6]
25-30 :	************ [high = 30]

Physics midterm problem: object distance with greatest magnification

Physics 205B Midterm 1, spring semester 2015
Cuesta College, San Luis Obispo, CA

Cf. Giambattista/Richardson/Richardson, Physics, 2/e, Problem 23.63

An object can be placed either 16 cm or 14 cm in front of a f = +15 cm converging lens. Decide which object distance will result in the largest image (regardless of being real/virtual, or inverted/upright), or if there will be a tie. Show your work and explain your reasoning using the properties of lenses, thin lens equations and/or ray tracings.

Solution and grading rubric:

• p:
  Correct. Compares the linear magnification ratios of both object distances using one of two methods:
  1. determines the image distances produced by these objects, then sets up the ratio m = –d_i/d_o to find their respective linear magnification factors;
  2. a carefully, properly scaled ray tracing diagram.
• r:
  Nearly correct, but includes minor math errors. May have sign errors or inverse errors.
• t:
  Nearly correct, but approach has conceptual errors, and/or major/compounded math errors. At least enough steps are shown that would theoretically result in a complete answer, multiple errors (or omission of last step of finding m = –d_i/d_o ratio) notwithstanding. May draw a ray tracing diagram that does not have its object distances properly scaled with regards to the focal points, but at least makes a consistent conclusion based on the faulty scaling of object positions.
• v:
  Implementation of right ideas, but in an inconsistent, incomplete, or unorganized manner. Ray tracings have real images for both cases, etc.
• x:
  Implementation/application of ideas, but credit given for effort rather than merit.
• y:
  Irrelevant discussion/effectively blank.
• z:
  Blank.
  

Grading distribution:
Sections 30882, 30883
Exam code: midterm01p34K
p: 21 students
r: 6 students
t: 13 students
v: 6 students
x: 1 student
y: 0 students
z: 0 student

A sample "p" response (from student 8984):

Physics quiz archive: lenses, optical instruments

Physics 205B Quiz 2, spring semester 2015
Cuesta College, San Luis Obispo, CA
Sections 30882, 30883, version 1
Exam code: quiz02r0cK



Sections 30882, 30883 results

0- 6 :
7-12 :	******* [low = 9]
13-18 :	*************
19-24 :	****************** [mean = 19.9 +/- 5.7]
25-30 :	************** [high = 30]

Physics quiz archive: lenses, optical instruments

Physics 205B Quiz 2, spring semester 2014
Cuesta College, San Luis Obispo, CA
Sections 30882, 30883, version 1
Exam code: quiz02O8Jt



Sections 30882, 30883 results

0- 6 :
7-12 :	*** [low = 11]
13-18 :	******
19-24 :	***************** [mean = 22.0 +/- 5.2]
25-30 :	************** [high = 30]

Physics midterm problem: microscope construction

Physics 205B Midterm 1, spring semester 2013
Cuesta College, San Luis Obispo, CA

Cf. Giambattista/Richardson/Richardson, Physics, 2/e, Problem 24.42

The converging lenses available from a commercial optics supplier have focal lengths f = +0.30 cm and f = +0.45 cm, respectively[*]. A Physics 205B student would like to use these two lenses to construct a microscope with a "tube length" L (the distance from focal point to focal point) of 5.0 cm, where the f = +0.30 cm lens is used as the objective. Solve for (a) the angular magnification of this microscope, and (b) the distance from the object to the objective lens. (The near point of the Physics 205B student is 25.0 cm.) Show your work and explain your reasoning.

[*] edmundoptics.com/optics/optical-lenses/double-convex-dcx-spherical-singlet-lenses/uncoated-double-convex-dcx-lenses/1748.

Solution and grading rubric:

• p:
  Correct. Determines (a) angular magnification to be –930×, and (b) the object must be placed 0.32 cm in front of the objective lens.
• r:
  Nearly correct, but includes minor math errors. Determines angular magnification, but does not explicitly solve for the distance for the object in front of the objective lens, but instead understands that it must be held very near outside the focal point (0.30 cm) of the objective lens.
• t:
  Nearly correct, but approach has conceptual errors, and/or major/compounded math errors. At least has magnification, and some attempt in finding the distance for the object in front of the objective lens
• :
  Implementation of right ideas, but in an inconsistent, incomplete, or unorganized manner.
• x:
  Implementation of ideas, but credit given for effort rather than merit.
• y:
  Irrelevant discussion/effectively blank.
• z:
  Blank.

Grading distribution:
Sections 30882
Exam code: midterm01p0C4
p: 19 students
r: 2 students
t: 4 students
v: 6 students
x: 2 students
y: 0 students
z: 0 students

A sample "p" response (from student 1224):

Physics quiz archive: lenses, optical instruments

Physics 205B Quiz 2, spring semester 2013
Cuesta College, San Luis Obispo, CA
Section 30882, version 1
Exam code: quiz02hYp0



Section 30882 results

0- 6 :
7-12 :	* [low = 12]
13-18 :	************
19-24 :	************* [mean = 20.5 +/- 4.9]
25-30 :	******* [high = 30]

Presentation: optical instruments

Look at them. Just look at them. Old school optical instruments: microscopes and telescopes.


Make sure you get a chance to look through them in class--use the pocket microscopes to look at laptop and smartphone screens, and the telescopes to look at the posters across the room. (Focus the microscopes using the ridged wheels, and focus the telescopes by sliding the eyepiece tube in or out.)

First, the similarities between microscopes and telescopes.

A microscope consists of a (short) tube that holds two lenses apart from each other: an objective lens in the front, and the eyepiece in the back.

Similarly, telescope consists of a (long) tube that holds two lenses apart from each other: an objective lens in the front, and the eyepiece in the back.

Let's look at the two-lens model of a microscope, where the objective is lens 1, and the eyepiece is lens 2. The objective takes the light from object, and creates a real image 1 (how do you know that this would be a real image?). This real image 1 then becomes the object 2 for the eyepiece.

Now let's look at the two-lens model of a telescope, where the objective is lens 1, and the eyepiece is lens 2. The objective takes the light from object, and creates a real image 1 (how do you know that this would be a real image?). This real image 1 then becomes the object 2 for the eyepiece.

Second, differences between microscopes and telescopes. (You may have started to notice some of them already.)

For the microscope ray tracing, the object 1 is placed just outside of the focal point of the objective, which makes a greatly enlarged real image 1. (Which ray tracing(s) ((1)-(10)) best match(es) this?)

Then this image 1 becomes the object 2 for the eyepiece, where it is placed on the focal point of the eyepiece to maximize its angular magnification. (Which ray tracing(s) ((1)-(10)) best match(es) this?)

(Strangely enough, the "tube length" for microscopes is defined as the distance measured between the objective and eyepiece focal points. Compare this definition to the "barrel length" for telescopes, below.)

Then for the telescope ray tracing, the object 1 is extremely distant, such that its rays are essentially parallel. The objective lens then focuses these parallel light rays onto an image 1 located at its focal point. (Which ray tracing(s) ((1)-(10)) best match(es) this?)

Then this image 1 becomes the object 2 for the eyepiece, where it is placed on the focal point of the eyepiece to maximize its angular magnification. (Which ray tracing(s) ((1)-(10)) best match(es) this?)

Where are the ray tracings for microscopes and telescopes most similar? Where do they differ?

(Note how 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. Compare this definition to the "tube length" for microscopes, above.)

Notice the negative sign in the angular magnification equations for microscopes and telescopes--what does this mean for the orientation of the final image seen through the eyepiece? Did you notice this for both the microscope and telescope?

What type of focal lengths would you want for the objective lens of a microscope? Telescope? What type of focal lengths would you want for the eyepiece lens of a microscope? Telescope?

The telescope angular magnification equation does not explicitly refer to the distance between the objective lens and the eyepiece lens. How is this distance related to the focal lengths f_o and f_e of the objective and eyepiece?

Presentation: magnifiers

Look at this magnifying glass. Just look at it. Um, through it.

In this presentation we will look through, um, at how magnifiers magnify. (In the next presentation we'll see how these magnifying lenses are used as eyepieces in telescopes and microscopes.)

First, defining what magnifiers do, and to what.

The angular size Θ is not the actual size, it is a measure of how large an angle it subtends with your eye at the origin, and is a measure of how big something "seems" from your viewpoint.

The angular magnification M (upper-case M, to distinguish it from linear magnification lower-case m) is a numerical factor denoting how much larger the angular size of something appears as seen through a magnifier, compared to with just the unaided eye.

When a converging lens with a focal length f is used a magnifier, the angular magnification is the ratio of the angular size as seen through the magnifier, compared to the angular size as seen with an unaided eye. This is also the ratio of the near point (the nominal closest distance an unaided eye can focus on, 25 cm) to the the focal length of the magnifier.

Second, the process of magnification using a magnifier.

Let's start with a rather provocative statement: a magnifying lens doesn't really magnify. Here we see a close-up (but unfocused) view of a pliers, and the same pliers at the same distance using a magnifying lens. The angular size of the pliers is relatively unchanged (after accounting for extreme defocusing circle of confusion blurring)!

Consider an Ames room, which is constructed that a person moving along the back of the room (which is actually greatly skewed) will be farther away or closer to an observer's eye, causing the person's angular size to change unexpectedly. This is the main idea behind angular magnification, which is merely caused by bringing an object closer to an eye.


Bringing an object closer to an eye increases its angular size, but there is a practical limit to how close an object can be brought such that the eye still can focus on it--the near point, with the nominal value being 25 cm. Any closer would still increase the angular size of the object, but the eye would no longer be able to focus clearly on it.


Now compare these two views of the pliers, without and with a magnifying lens. Note that without the magnifying lens, the view is focused at ∞, where objects on the horizon are sharply in focus, and the pliers is out of focus. With the magnifying lens, the view is still focused at ∞, but now the pliers is in focus, meaning that the virtual image produced by the magnifying lens is at ∞. (How do you know that this is a virtual image? Which ray tracing best matches this?) This is because the pliers is on the focal point of the magnifying lens, which produces a virtual image (of the same angular size) out at infinity.

So to refine our understanding of what magnifiers actually do:

• The maximum angular size of an object as seen by an unaided (nominal) eye is when the object is placed 25 cm away.
• For a magnifying lens with a focal length f of less than 25 cm, the object can then be brought closer (up to the focal point of the magnifying lens), such that the magnifying lens allows the eye to be able to focus (at ∞) on an object held closer than 25 cm.
• Closer is bigger.

One could also think of the magnifying glass as increasing the accommodation ability of the eye to focus on objects nearer than 25 cm, such that objects can be brought closer in order to increase their angular size.