## Get All Weeks First Order Optical System Design Coursera Quiz Answers

This course can also be taken for academic credit as ECEA 5600, part of CU Boulder’s Master of Science in Electrical Engineering degree.

Optical instruments are how we see the world, from corrective eyewear to medical endoscopes to cell phone cameras to orbiting telescopes. When you finish this course, you will be able to design, to first order, such optical systems with simple mathematical and graphical techniques.

This first-order design will allow you to develop the foundation needed to begin all optical designs as well as the intuition needed to quickly address the feasibility of complicated designs during brainstorming meetings. You will learn how to enter these designs into an industry-standard design tool, OpticStudio by Zemax, to analyze and improve performance with powerful automatic optimization methods.

### Week 01: First Order Optical System Design Coursera Quiz Answers

#### Quiz 1: Snell’s Law Practice Problem

Q1. An thin beam of white light with negligible radius is incident at 50.0° on 10.0 cm thick slab of clear plastic. The index of refraction for red light in this material is 1.51 and for violet light it’s 1.54. Determine the approximate diameter, DD, of the emerging beam. Express your answer in cm with two significant figures.

A diagram of the problem is shown below. It is labeled with some possibly useful variables, but feel free to do the problem in any way that makes sense to you.

Enter answer here

#### Quiz 2: Practice problems

Q1. A beam of light is incident upon an equilateral prism with index of refraction of 1.5, pictured below.

At what angle does the beam of light exit the prism, measured with respect to the normal to the exiting surface of the prism? Enter your answer in degrees.

As an additional exercise, also trace some of the reflected beams as they travel through the prism.

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Q2. For the above prism problem, what would happen if the index of refraction of the prism was 1.55? This is a reflective thought problem. We are not looking for a numerical answer here, but rather a thoughtful response.

What do yoou think?

#### Quiz 3: Rays and Snell’s Laws

Q1. In which of the following situations is the ray equation valid for evaluating optical systems? Choose all correct answers.

- A plane wave refracting at an infinite flat surface.
- The focus of a lens with a plane wave input.
- A plane wave refracting through the center of a lens.
- The edge of a plane wave traveling through a pinhole.

Q2. The following image shows equiphase surfaces of an optical wave (wavefronts) before (a) and after (b) an interface. What can you deduce about the interface from the image of the wavefronts? Draw some rays to help you.

- The interface is a flat surface.
- The interface is a concave curved surface.
- The interface is a convex curved surface.
- The index of refraction to the right of the interface is higher than to the left.
- The index of refraction to the right of the interface is lower than to the left.

Q3. The following image shows equiphase surfaces of an optical wave (wavefronts) before (a) and after (b) an interface. What can you deduce about the interface from the image of the wavefronts? Draw some rays to help you.

- The interface is a flat surface.
- The interface is a concave curved surface.
- The interface is a convex curved surface.
- The index of refraction to the right of the interface is higher than to the left.
- The index of refraction to the right of the interface is lower than to the left.

Q4. The following image shows equiphase surfaces of an optical wave (wavefronts) before (a) and after (b) an interface. What can you deduce about the interface from the image of the wavefronts? Draw some rays to help you.

- The interface is a flat surface.
- The interface is a concave curved surface.
- The interface is a convex curved surface.
- The index of refraction to the right of the interface is higher than to the left.
- The index of refraction to the right of the interface is lower than to the left.

Q5. When a ray of light traveling in air hits a tilted plane parallel slab (of glass, say), it emerges parallel to the original ray but shifted transversely. Carefully draw out the situation and use Snell’s law to derive the amount of the transverse shift, xx, as a function of the tilt angle of the slab, \thetaθ, its thickness, dd, and its index of refraction, nn. Find the exact expression with no approximations.

We recommend you do this out all in variables because it’s a useful formula to have. Also, you will want this for the following questions. However, since the auto-grader has difficulty with these formulas, use n = n=1.5, d = d=1.0 cm, and \thetaθ = 45° and enter a numerical answer. Give your answer in cm to two significant figures.

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Q6. Using your results from the previous question, derive the paraxial, small angle, expression for the transverse shift, x. Give your answer in terms of d, \thetaθ, and n.

If you are not familiar with the paraxial approximation, take a look at the Wikipedia article or another online source. As a short summary, for small angles, \sin{\theta} \approx \thetasinθ≈θ, \tan{\theta} \approx \thetatanθ≈θ, \cos{\theta} \approx 1cosθ≈1, and \theta^2 <<1θ

2

<<1.

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Q7. Using your drawings and results from questions 5 & 6, consider a cone of rays converging toward a perfect focus. Now insert a slab of glass, normal to the optic axis, somewhere before the focus. Start with a good sketch of the problem. Which of the following statements are true? Pick all true statements.

- The focus shifts toward the glass.
- The focus shifts away from the glass.
- All angles incident on the glass focus at the same location.
- Higher angles focus farther from the glass then lower angles.
- Lower angles focus farther from the glass than higher angles.

Q8. For the situation in question 7, how much does the focus shift along the axis? Calculate this for the non-paraxial case (no approximations). Express your answer in \thetaθ, d, and n as defined in problem 5.

Then, for ease of grading, using the same values as in question 5: n = 1.5, d = 1 cm, and \thetaθ = 45° and enter a numerical answer. Express your answer in cm to two significant figures.

Enter answer here

Q9. Consider an optical disk drive with a lens focusing a collimated beam into a mm-thick disk with an index of refraction of n. If the lens moves towards the disk a distance, t, how much does the focus shift inside the material? Assume the paraxial approximation and that the focus remains inside the material (i.e. t is not far enough to move the focus past the material). Express your answer in terms of the two given variables.

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Enter math expression here

Q10. A group of students wanted to watch the solar eclipse, but were unable to get eclipse glasses. They decided to build a pinhole projector out of a cardboard box. They would like the image of the sun to be at least 2.0 cm in diameter. If the pinhole is on one end of the box, and the screen on the other, how long should the box be? Enter your answer in meters to two significant figures.

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Q11. While outside watching the projection of the eclipse with their very nice pinhole projector, the students noticed images of the eclipse on the ground under the tree nearby:

The images were not only larger than their pinhole projection, but there were many images of the sun to see all at once.

What were they seeing and why? Draw out a ray diagram and describe in words what is causing this image above?

One student took out a ruler and measured the image of the sun on the ground to have a diameter of 6.0 cm. Approximately how tall was the tree? Enter your answer in meters with two significant figures.

Enter answer here

### Week 03: First Order Optical System Design Coursera Quiz Answers

#### Quiz 1: Practice problem

Q1. Two brightly lit objects are imaged onto a screen by a converging lens as

shown. A

mask is used to cover up the bottom half of the lens, as shown. What happens to the images on the screen when

the mask is inserted over the bottom half the lens?

What do you think?

#### Quiz 3: Ray Tracing and Lens Analysis

Q1. A green arrow acts as the object to be imaged by a positive focal length lens, as shown below. The clear circles indicate the location of the front and back focal planes of this thin lens. Each square below is 1 cm x 1 cm. Draw the principle rays to find the image.

What is the location of the image? Enter your answer in cm. Note that in all questions with numerical answers, a range of values is accepted to account for small round off or (as in this case) estimation variations. If you use an appropriate number of significant figures for each problem, the range should be sufficiently large to accept your answer.

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Q2. For the previous question, what is the size of the final image? Enter your answer in cm.

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Q3. Is the image real or virtual? Is it upright or inverted?

- Real
- Virtual
- Inverted
- Upright

Q4. A green arrow acts as the object to be imaged by a positive focal length lens, as shown below. The clear circles indicate the location of the front and back focal planes of this thin lens. Each square below is 1 cm x 1 cm. Draw the principle rays to find the image.

What is the location of the image? Enter your answer in cm.

Enter answer here

Q5. For the previous question, what is the size of the final image Enter your answer in cm.

Enter answer here

Q6. Is the image real or virtual? Is it upright or inverted?

- Real
- Virtual
- Inverted
- Upright

Q7. A 35-mm camera has a single thin lens having a 50.0-mm focal length. A woman 1.65 m tall stand 5.0 m in front of the camera. What is the distance between the lens and the film when she is in focus? Enter your answer in mm.

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Q8. For the previous problem, how tall is the image of the woman on the film? Enter your answer in mm as a positive number.

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Q9. A spherical mirror forms an erect image that is 1/3 the size of the object. What is the mirror curvature? Concave (center of sphere is on the same side as the object) or convex (center of sphere is on the opposite side of the mirror from the object)?

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Q10. For the previous problem, if the object is 100 cm from the vertex (the point where the mirror meets the optic axis), determine the image distance t’. Express your answer in cm. Remember the sign convention.

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Q11. Let’s now look at a real lens example. You want to design a system with a microscope objective. Start out with the objective: you have a 20X objective, with a 160 mm tube length. The magnification is 20X, and the tube length is the distance from the image to the back focal point. What is the focal length of the objective lens? Express your answer in millimeters with 2 significant figures.

Hint: the Newtonian form of the lens equation is helpful here. Also, you may want to learn more about microscope objectives, for example Thorlabs has a tutorial.

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Q12. For the objective described in Question 11, what should the object distance be to get the 20X magnification? Express your answer in millimeters with 2 significant figures.

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Q13. Generally, in a microscope, you will have an additional eyepiece for relaying the image from the microscope object to the eye or a camera tube lens to image onto a camera. We will learn more about the eye in a later course in this series, so for now, plan on having a camera tube lens with a magnification of 0.75X. If imaging a sample with 10 \mu mμm features, how large will they appear on the camera? Express your answer in \mu mμm with 3 significant figures.

Enter answer here

### Week 04: First Order Optical System Design Coursera Quiz Answers

#### Quiz 1: OpticStudio practice

Q1. This is an opportunity to get some extra practice with OpticStudio.

Load the

OpticStudio example file Samples/Sequential/Miscellaneous/

Mangin

mirror.ZMX. This shows what the Mangin mirror looks

like in OpticStudio. Calculate the focal

length of this system (note that the units are specified as mm). You can use the “Surface Data” report to find

the refractive index of BK7 at the operational wavelength.

Enter answer here

Q2. Why are thicknesses after the mirror specified as negative numbers?

What do you think?

#### Quiz 2: Thick Optics Practice Problems

Q1. Determine the focal length in air of a thin (negligible thickness) spherical

planar-convex lens having a radius of curvature of 50.0 mm and an index of

1.50. Enter your answer with units of cm to one decimal place.

Enter answer here

Q2. For the previous problem, what, if anything, would happen to the focal length if the lens were placed in a tank of water? Enter the focal length of this lens in water in units of cm to one decimal place.

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Q3. An equiconvex lens has curvatures of -c1 = c2 = -0.5 (1/cm). How thick must the

lens be for its power to be zero if the index of the lens material is 1.5. Express your answer in cm to one decimal place.

Enter answer here

#### Quiz 3: Thick Optics

Q1. Two positive thin lenses are separated by a distance of 5.00 cm. The focal lengths of the lenses are F1 = 10.0 cm and F2 = 20.0 cm. Using ray tracing along with numerical methods, determine the power of the combination in 1/cm. Express your answer with three significant figures.

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Q2. What is the back focal distance of the two lens system described in question 1, in cm? Express your answer with 2 significant figures.

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Q3. What is the front focal distance of the two lens system described in question 1, in cm? Express your answer with 2 significant figures.

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Q4. What is the location of the front principle plane of the two lens system described in question 1, measured relative to the first lens, in cm?

If the front principle plane is to the left of the first lens (before the lens), enter you answer as a negative number; if it is to the right of the first lens (after the lens), enter your answer as a positive number. Express your answer with 2 significant figures.

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Q5. What is the location of the back principle plane, measured relative to the first lens again, in cm? If the back principle plane is to the left of the first lens (before the lens), enter you answer as a negative number; if it is to the right of the first lens (after the lens), enter your answer as a positive number. Express your answer with 2 significant figures.

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Q6. If an object is placed 2.0 cm to the left of the front focal point, where is the image located relative to the back focal point? Express your answer in cm. Express your answer with 2 significant figures.

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Q7. What is the magnification of the image for the situation described in question 6? Express your answer with 2 significant figures.

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Q8. What is the throw of the system described in question 6? The throw is defined as the distance between the object and the image. Express your answer in cm, with 2 significant figures.

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Q9. Go to the Newport website (https://www.newport.com) and find bi-convex, N-BK7 lenses with a 50.8 mm diameter with 10.0 cm and 20.0 cm effective focal lengths. Insert these into your system instead of the thin optical lenses so that you get the same image with the same object 2.0 cm to the left of your front focal point. What is the throw of your system now? Express your answer in cm, with three significant figures.

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Q10. What is the distance between the back surface of your first lens and the front surface of your back lens using the real lenses described in question 9? Express your answer in cm, with three significant figures.

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Q11. You have a client who is interested in selling swim goggles for myopic triathletes who need to be able to see long distances while swimming in open water. The goggles need to perform as glasses for the swimmers while under water as well as when they are looking in air.

Think about what it means to be myopic, draw out the rays, and decide what type of lens (converging or diverging) would be needed.

What is the shape of the lens that you must use if the lens is made of a single, constant index material?

- Biconvex.
- Planoconvex, flat surface closest to the eye.
- Planoconvex, curved surface closest to the eye.
- Planoconcave, curved surface closest to the eye.
- Planoconcave, flat surface closest to the eye.
- Biconcave.

Q12. For a myopic swimmer with a prescription of -7.0 diopters, what should the radii of curvature of the lens surfaces be if the goggles are made from a high index plastic of n = 1.6? First, what is the radius of curvature of the outer surface (furthest from the eye)? If the surface is flat, enter ‘i’ for an infinite radius.

Express your answer in cm and round to a single decimal place.

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Enter math expression here

Q13. For the myopic swimmer with a prescription of -7.0 diopters, what should the radii of curvature of the lens surfaces be if the goggles are made from a high index plastic of n = 1.6? First, what is the radius of curvature of the inner surface (closest to the eye)?

If the surface is flat, enter ‘i’ for an infinite radius.

Express your answer in cm and round to a single decimal place.

Preview will appear here…

Enter math expression here

### Week 05: First Order Optical System Design Coursera Quiz Answers

#### Quiz 1: OpticStudio practice

Q1. This is an opportunity for you to get some more practice with OpticStudio.

Load the OpticStudio example file Samples/Sequential/Afocal/Beam Expander.ZMX. Is this a Keplerian or a Galilean telescope? How can you tell from the layout that this is an afocal system?

What do you think?

#### Quiz 2: yu Tracer & ABCD Matrix Practice

Q1. The conjugate matrix for a two lens system is given by:

If the focal length of the first lens is 20 cm and the focal length of the second lens is 40 cm, what is the distance between the lenses (in cm)?

Enter answer here

Q2. For the previous problem, what is the magnitude of the object distance, t_1t, in cm?

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Q3. For the previous questions, what is the image distance, in cm?

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#### Quiz 3: yu Tracer and ABCD Matrices

Q1. Create your own yu ray tracer. A spreadsheet is convenient, but this is your tool, so use whatever works best for you. The program should fundamentally work on paraxial lens powers and spacings. You will need the ability to trace both forwards and backwards through a system.

The focal lengths of the four lenses are f_1 = 100 mmf

1

=100mm, f_2 = -50.0 mmf

2

=−50.0mm, f_3 = 80.0 mmf

3

=80.0mm and f_4 = -280 mmf

4

=−280mm. The separation between the lenses are t_1 = 20.0 mmt

1

=20.0mm, t_2 = 40.0 mmt

2

=40.0mm, and t_3 = 30.0 mmt

3

=30.0mm.

Where is the image located if the object is 400 mm from the first lens? Express your answer in mm using three significant figures.

Enter answer here

Q2. For the previous question, what is the magnification of the system? Express your answer with three significant figures.

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Q3. An optical resonator consists of two identical concave mirrors as shown below:

Calculate the ABCD matrix for one full round trip through this system, starting on the left, traveling to the first mirror, then reflecting, traveling to the second mirror, and reflecting (4 matrices). Give your answer in terms of the distance between the mirrors, d, and the radius of curvature of the mirrors, r.

This may be easier to think about as a two-lens system, where you start a distance d from the first lens, travel through that lens, a distance d to the second lens and through that lens.

This is a straightforward matrix multiplication problem but be careful to go slowly and keep track of all terms and signs. You may also do this in a symbolic mathematical program if you prefer.

First list the 11 element of the matrix you calculated (top left element).

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Q4. Now list the 12 element of the matrix you calculated (top right element).

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Q5. Now list the 21 element of the matrix you calculated (bottom left element).

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Q6. Now list the 22 element of the matrix you calculated (bottom right element).

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Q7. Two positive thin lenses are separated by a distance of d. The focal lengths of the lenses are f_1 = 10.0 cm f

1

=10.0cm and f_2 = 20.0 cmf

2

=20.0cm. The desired throw of the system, the object to image distance, is T = 80.0 cmT=80.0cm and the desired magnification is M = -1.10xM=−1.10x.

Use what you know about the conjugate matrix for a two lens system to solve to the distance between the lenses. Express your answer in cm with three significant figures.

This and the following problems require some significant algebra. While not required, you are welcome to use a program such as Matlab for these problems. You will find two possible solutions to this and the following problems. Either is acceptable.

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Q8. For the previous questions, where should be the object be placed? Express the distance between the object and the first lens in cm with three significant figures.

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Q9. For the previous question, where will the image be found – what is the distance between the image and the second lens in cm? Express your answer with three significant figures.

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##### Conclusion:

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This course is intended for audiences of all experiences who are interested in learning about new skills in a business context; there are no prerequisite courses.

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