Thin Lenses

Overview

In this lab simulation, you will see the relationship of the object distance, the image distance, and the focal length of a lens. The relationship between these quantities is shown in thin lens equation below. At the end of the simulation, you will be able to understand how the position of the image changes due to the change in position of the object and the change in curvature of the lens which affects the focal length. You also understand how the image size and nature of the image would be affected due to the change in position of the object. In general the thin lens equation makes perfect sense with this simulation. In this simulation, the three ray system (parallel-focal, focal-parallel, central) can be used to construct the image. The lens used is a thin double-convex lens.

Important formulas    

where f is focal length, p is the object distance, q is the image distance, R is the radius curvature, h_i is the image height, h_o is the object height, n is the refractive index of the lens, and m is the magnification.

Read Ch 23: Sec 1-4 for concepts.

Simulation:  Open Geometical

https://phet.colorado.edu/sims/geometric-optics/geometric-optics_en.html               

Take a few minutes to be familiar with the simulation. You are able to move the object and the lens and change the characteristics of the lens. During this lab, be sure to always anchor your image on the principal axis.

·         Check on a Ruler whenever you need to measure distances

·         Check the principal rays to draw the rays with the three ray system learned in class

1. What happens to the image formed on the other side of the lens when the object

a. moves up and down? ________

b. moves away from the lens? _________

c. moves towards the lens (not passing the focal point, x)? __________

d. is right at the focal point. Describe/sketch the refracted rays that emerge on the other side of the lens. ___________

e. moves towards the lens past the focal point? What happens to the rays after they pass through the lens? Do they Converge or Diverge? Do you see the image? If not, why?

If you didn’t see the image, will you be able to locate where the image is supposed to be geometrically? If so, sketch it. What is the nature of image?

2. While your object is between the focal point and the lens, click on “virtual image” and describe your observation. If you see the image, describe its location, size as compared to the object, and its similarity and difference with the real image.

3. Verify the focal length of the lens:

a. Set the refractive index (n) to 1.5 and the radius of curvature (R) to 0.6 m. Use the appropriate equation to calculate the focal length (f) of the lens

f = ________________________________

b. Measure the focal length of the lens to confirm your answer. If it is different from your calculated response, why?

4. Use the focal length you found in (3), complete the table below and check your work in the simulation.

5. Repeat step 4 for a lens with different property. The refractive index of the lens is 1.6 and radius of curvature of 0.8. Remember to find out the focal length first.

 f = ___________

6. Set the refractive index (n) to 1.5 and the radius of curvature (R) to 0.6 m. Position the object so that the image is formed 100 cm to the right of the lens (use ruler). Is the image enlarged or reduced in size?

Size: _______

What is the object position (use ruler) ? ___________

What is the magnification?  __________

Now keeping the object and ruler fixed (between lens center and image position at 100 cm), adjust the LENS position (move it left or right) so that the image is again formed in the same place as before (i.e. at the same mark on the ruler as before).

What are the new object and image positions? Use the ruler to measure. _____

Is the image enlarged or reduced in size? ______

Do you observe a relationship between the new object and image position vs the old object and image positions? What is this relation? Explain why this is so.

Conclusion questions and Calculations:

1. Images found on the opposite side (as the object) of a lens are real / virtual images that will be upright / inverted.

2. As the radius of curvature of the lens increases, the focal point of that lens becomes closer to / further away from that lens.

3. As the refractive index of the lens increases, the focal point of that lens becomes closer to / further away from that lens.

4. What advantage does a larger lens have over a smaller lens (all other characteristics being equal)?

5. What was the focal distance (f ) when the radius of curvature was 0.8 and index of refraction was 1.6? _____________

6. Calculate the radius of curvature of a lens with a focal distance of 40.0 cm and an index of 1.2. __________________

7. An object placed 3cm away from a lens projects a real image 0.6m behind the lens. What is this lens focal distance? _____________________

8. What is the lens magnification? ____________________

9. An object 20.0 cm to the left of a convex lens is 1.0 m in height. What is the height and location of its image if the lens has a magnification of -2.0?

_____________ m and _______________cm on the left / right side of the lens.

 What is the focal length of the lens?   ____________

10. Imagine you are nearsighted. In order to correct your vision, you need glasses with a converging / diverging lens. Explain your answer.

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