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 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 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 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: thin lens equations

So far we have used ray tracings to analyze images created by converging and diverging lenses. In this presentation we will qualitatively analyze lenses using the thin lens equations.

First, relating the locations of the object and image for a lens.

The convention in ray tracings is for light to move from left-to-right, with the object located to the left of the lens, and the image (if real) would be located to the right of the lens. For this case the object distance d_o and the image distance d_i would both be positive. If the image is virtual, then it would be located to the left of the lens, and the image distance d_i would then be negative.

The thin lens equation relates the object distance d_o, image distance d_i, and lens focal length f.

The focal length f is defined to be positive for a converging lens, and negative for a diverging lens, and d_o and d_i follow the sign conventions discussed above. (For the sake of completeness, there is such a thing as a "virtual object," but will not be considered in this course.)

Second, linear magnification.

Linear magnification m is defined as the ratio of the image height compared to the object height. The linear magnification can be either positive or negative, depending if the image is upright compared to the original object, or inverted compared to the original object. This ratio of image versus object heights is also equal to the ratio of image versus object distances (with an obligatory negative sign).

So for an upright image, m is a positive quantity, regardless of being enlarged or diminished.

And for an inverted image, m is a negative quantity, again regardless of being enlarged or diminished.

The absolute value of linear magnification m is greater than 1 if the image is enlarged, regardless of being upright or inverted.

And for a diminished image, the absolute value of linear magnification m is less than 1 if the image is enlarged, regardless of being upright or inverted.

Picto-quiz: lenses and images

Let's apply the concepts introduced in a previous presentation, where we used ray tracings to find images produced by converging and diverging lenses.

Pair up in groups of two or three, pick up a whiteboard, and for each of these real-world examples, decide whether this is a converging or diverging lens, producing a real or virtual image, and choose the corresponding ray tracing diagram (or diagrams) from your worksheet.

For this image produced by a water glass, is this produced by a converging or diverging lens? Is this a real or virtual image? Which ray tracing(s) ((1)-(10)) best match(es) this?

How do you know this?

For this image produced by a camera lens attachment, is this produced by a converging or diverging lens? Is this a real or virtual image? Which ray tracing(s) ((1)-(10)) best match(es) this?

How do you know this?

For this image produced by magnifying glass, is this produced by a converging or diverging lens? Is this a real or virtual image? Which ray tracing(s) ((1)-(10)) best match(es) this?

How do you know this?

For this image produced by a pair of glasses, is this produced by a converging or diverging lens? Is this a real or virtual image? Which ray tracing(s) ((1)-(10)) best match(es) this?

How do you know this?

For this image on a frosted glass screen produced by a lens on an optical bench, is this produced by a converging or diverging lens? Is this a real or virtual image? Which ray tracing(s) ((1)-(10)) best match(es) this?

How do you know this?

For this image produced by a door peephole, is this produced by a converging or diverging lens? Is this a real or virtual image? Which ray tracing(s) ((1)-(10)) best match(es) this?

How do you know this?

For this image produced by a glass paperweight, is this produced by a converging or diverging lens? Is this a real or virtual image? Which ray tracing(s) ((1)-(10)) best match(es) this?

How do you know this?

For this image produced by a slide projector, is this produced by a converging or diverging lens? Is this a real or virtual image? Which ray tracing(s) ((1)-(10)) best match(es) this?

How do you know this?

Presentation: lenses

Look at these images. Just look at them. Reach for them, and touch them if you can. (These are actually real and virtual images produced by a spherical mirror at the Reuben H. Fleet Science Center, San Diego, CA.) (Video link: "080724-1040074.")

Although mirrors create images as well, we will instead focus our attention on images created by lenses.

Whereas mirrors create images by reflecting light off of their surfaces, lenses create images by refracting light through their front and rear surfaces. As a result of shaping these surfaces, two different types of lenses can be made.

First, properties of these two different types of lenses.

A converging lens will take parallel rays of light (here, from the sun) and bring them to a focus at a point in space.

A diverging lens will take parallel rays of light and "defocus" them (spread outwards) away from a point in space.

The focal point of a lens is the location in space where parallel light is brought to a focus (for a converging lens), or the location in space where parallel light is made to spread outwards from (for a diverging lens).

Second, developing a graphical model of how these lenses generate images.

Although a converging lens is a physical object with curved surfaces, our model assumes that thickness of the lens is unimportant, so we merely indicate its convex surfaces with curved top and bottom bars.

We are going to draw three principal rays for this converging lens that start from an object placed to the left of the lens (convention is that light will travel from left-to-right across these ray tracing diagrams). There are many other light rays that can be drawn, but these three principal rays should suffice to locate the image (if any) generated by this lens. (Ideally you would only need to draw two rays to locate the image at their intersection (if any), but we'll draw a third principle ray as a redundant check.)

The principal rays for a converging lens all start from the top of the object.

1. Ray travels horizontally, and the converging lens will redirect this ray through its focal point on the right.
2. Ray travels straight through the center of the lens, and continue onwards.
3. Ray travels through the focal point on the left, and the converging lens will redirect this ray horizontally.

We will practice drawing these converging lens ray diagrams for different object distances, and locate the subsequent images generated by the intersection of these principal rays on a worksheet in class. There will be subtleties not covered in these principal ray rules, but the worksheet will handle all of these special cases.

Note the symbol used here for a diverging lens--again, the thickness of the lens is unimportant, so we merely indicate its concave surfaces with curved top and bottom bars.

The principal rays for a diverging lens all start from the top of the object.

1. Ray travels horizontally, and the diverging lens will redirect this ray out away from its focal point on the left. Draw a dashed line that traces back to the focal point, indicating that for an observer on the right of the lens, the redirected ray appears to have come from the focal point on the left.
2. Ray travels straight through the center of the lens, and continue onwards.
3. Ray travels towards the focal point on the right, and the diverging lens will redirect this ray horizontally. Draw a dashed line that traces back horizontally, indicating that for an observer on the right of the lens, the redirected ray appears to have always traveled horizontally.

Again, we will practice drawing diverging lens ray tracings for different object distances, and locate the subsequent images generated by the intersection of these principal rays on a worksheet in class.

Third, the two different types of images that can be generated. These will be demonstrated by mirrors, but images generated by lenses will have the same certain attributes.

(Video link: "REFLECTIONS: Giant Spherical Mirror Tricks.") If the redirected rays of light actually intersect at a location in space, then a real image is generated. At certain viewing angles, the real image amy literally seem "float" in space at this location, and a screen can be placed at this location to show that the light rays actually intersect there.

(Video link: "Milo's Mirror.") If the redirected rays of light do not actually intersect at a location in space, but merely move outwards from an extrapolated location (here, behind the mirror), then a virtual image is generated. At certain viewing angles, the virtual image seem to be located at a point in space, but a screen cannot physically be placed at this location (which would here be behind the mirror) to show that the light rays actually intersect there.

Again, these distinguishing properties of real and virtual images are here demonstrated by mirrors, but real and virtual images generated by lenses have these same properties. These will become more apparent after completing the ray tracing worksheets below, more quantitative discussion of lenses in a subsequent presentation, and experiencing these images hands-on in open-ended labs.

This worksheet (consisting of five converging lens and five diverging lens ray tracings) will illustrate all the possible unique ray tracings for converging and diverging lenses. Neatness counts, so this is also a test of your drafting skills. You should be able to draw any and all of these ray tracings to scale for your homework, and on the quiz as well.

After completing each of these ray tracings, indicate whether the resulting image (if any) is upright or inverted (with respect to the original object), enlarged or diminished (with respect to the original object), and is real or virtual (located at an actual intersection of principal rays, or located at a backwards-extrapolated intersection of principal rays). Refer to this worksheet when we look at real-world examples of these images in a picto-quiz.

For reference, solutions to the worksheet are shown below. For the purposes of the quiz, make sure you would be able draw any and all of these ray tracings without referring to the solutions.