9 Lab 4 – Geometric Optics

Acknowledgment

This project is made possible with funding by the Government of Ontario and through eCampusOntario’s support of the Virtual Learning Strategy. To learn more about the Virtual Learning Strategy visit: https://vls.ecampusontario.ca.

PHY137 Stay-At-home Experiment 4

Geometric Optics

What you will do

Explore the reflection and refraction of light through a prism. Then build a telescope and a microscope using two convex lenses.

What you will need

• A prism
• A cell phone with a flashlight (or a regular flashlight).
• A pair of lenses with different focal lengths
• A non-transparent cardboard box with at least one dimension between 10~20 cm
• Several pieces of cardboard
• A knife or a pair of scissors
• Some tape
• A pen or a pencil
• A ruler

Demonstration Video: https://youtu.be/EAPoTWajx98

Procedures

Part I – reflection and refraction of light

1. Make a light-sheet light ray with the cardboard box and your cell phone. Pick two opposing surfaces on your box that are between 10~20 cm apart. Use a knife or a pair of scissors to cut open a small 3cm x 3cm window near the bottom edge on one of the surfaces. Then on the opposite surface at approximately the same location, cut open a 3mm x 4cm narrow vertical slit. (You will also need this box in Lab 5.)
2. Turn on the flashlight of your cell phone, attach the phone to the window on the box so that the light ray exits the slit on the opposite side as a light sheet.
3. Tape or strap the phone to the cardboard to stabilize them. Place the light source on a flat surface. Make sure the beam is visible for at least 20cm without spreading out too much. You may turn off the room lights and close the curtain to improve visibility of the beam.
4. Place a prism in the light beam with one of the square surfaces facing the light, and the triangle edges on the top/bottom. Rotate the prism and watch the light ray being reflected and refracted.
5. Place a piece of white paper under the prism. Turn the prism so that the incident light ray is tilted relative to the front surface like in the figure below. Mark the position of the prism and trace all light rays (including reflections and refractions) on the paper.
6. Place another piece of white paper under the prism. Turn the prism slightly so that the light rays are still refracted twice by the prism, but at different angles from the previous step. Mark the position of the prism and trace all light rays (including reflections and refractions) on the paper.
7. Use your sketches to measure the angles of incidence and the angles of refraction. Label the angles on your sketch. If you do not have a protractor, you can attach your paper to a vertical wall, and use the inclination tool in the Phyphox app to find the angles. (Subtracting any two tilt angles will yield the angle in between two different tilts.)
8. Use the angles of incidence and the angles of refraction to calculate the index of refraction of the prism. (Four refraction events for four calculations of indices.) Take the average of the four indices of refraction as the measured value, and their standard deviation as the uncertainty.
9. Calculate the critical angle at which light rays can undergo total internal reflection inside the prism.
10. Place another piece of white paper under the prism. Turn the prism until the light ray is at normal incidence on the surface of the prism (but not centered). Mark the shape of the prism and trace all light paths on the paper.
11. Measure the angle of incidence and the angle of reflection at the point of internal reflection to verify that the condition for total internal reflection is met.
12. Scan all your sketches and attach them in your lab report for reference.

Part II – lenses, telescope, and microscope

1. The two lenses that come with the lab kit have different focal lengths. Place one of the lenses between a distant light source and a flat white surface. (The light source can be any far and bright object, such as a lamp on the ceiling, the Sun, or your window during the day). Adjust the distance between the lens and the white surface till you see a clear image of the light source.
2. The distance between the lens and the image is close to the focal distance of the lens. Measure the focal distance of both lenses in this way. For both lenses, use your phone to take photos of the lens and a clear image of the light source behind the lens. Attach these photos in the lab report for reference.
3. Cut off two pieces of cardboard that are about 10cm by 10cm in size, cut a window that is slightly smaller than the lens on each cardboard. Tape each lens to cardboard. (Do not tape through the center of the lens. You need to see through the center.)

<<For the sections below, you only need to complete one of the two instruments of your choice – either the telescope or the microscope. If you choose to complete one of them, you must discuss why you think the other one is more difficult to construct/complete.>>

1. [Telescope] Hold the lens that has the shorter focal length (the “eyepiece”) to your eye, hold the other lens (the “objective”) farther away. Try to adjust the distance between the lenses while looking through both lenses. When the distance is just right, you will see a clear, inverted, and magnified image of a distant object through the two lenses. What do you expect the separation of the lenses to be when they form a telescope?
2. [Telescope] Tape the two lenses to two boxes (or any solid object with a vertical face). Adjust the separation of the two boxes until the lenses are separated the same way as you did in the previous step. Use your phone camera to take a picture of a distant object that you can see through the telescope. Zoom in about 4X on your camera app so that the farther lens takes up more of the photo.
3. [Telescope] Calculate the theoretical angular magnification of your telescope.
4. [Microscope preparation] Hold the lens with the shorter focal length close to an object. Look through the lens. Depending on the distance between the lens and the object, you should see either a magnified upright image, or a magnified inverted image. What is the condition for you to see an upright image? What is the condition for you to see an inverted image?
5. [Microscope] Fix the lens that has the shorter focal length (the “objective”) at a distance that is slightly larger than the focal length of the objective. You can use any stable object that has a height more than the focal distance as the stand. Note that if you look through the objective lens, the central region of the image is magnified but inverted and not clear. (If it is clear and upright, you are at a wrong distance.) Hold the other lens (the “eyepiece”) to your eye. Adjust the distance between the eyepiece and the objective, you will notice that the central region of the image becomes magnified and clear (but still inverted).
6. [Microscope] line up the eyepiece lens with your phone’s camera lens. Zoom in about 4X on your phone app. Take a photo of some texture that is smaller than 1mm (such as the fabric of a cloth, ink on a piece of paper, etc.) through your microscope.

Tips for data analysis:

• Complete all measurements and calculations that are required in the procedures above. Show sample calculations in the appendix.
• Attach all photos that are required in the procedures above.
• Answer all questions in the procedures above.
• Attach graphs or tables when necessary.

Suggested topics for discussion:

• Find the uncertainty values for each calculation in the results section. Show a sample calculation of your error propagation in the appendix.
• Identify the sources of error in your measurements.
• Feel free to do more tests to verify your claims if possible.
• Make a reasonable conclusion based on your results.
• What other quantities can be determined with the same experimental design?
• What can be done to reduce the uncertainties at no cost while staying at home?

We value your feedback!

Did you enjoy this experiment? What are the aspects that you dislike the most about this experiment? – Let me know in the “Student Feedback Survey for Lab 4” on the discussion board on Quercus! We may award the most helpful inputs with +1 bonus mark for the lab report!

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