PHYS 1402 – General Physics II

The Simple Magnifier

Materials

Ruler

100 mm lens

150 mm lens

250 mm lens

-150 mm lens

Introduction

In this brief activity we will explore a few basic properties of the human eye and apply them to a magnifying glass, or what we call a simple magnifier.

The Relaxed Eye

1. Have someone in your group, preferably with uncorrected vision, relax with their eyes open, not look at anything directly. Now ask the member of the group where are they looking?

Record the answer.

2. Try with several other members of the group.

Record their responses.

3. The answers may have been something like, "nowhere", "off into space", "the wall", "the ceiling". In terms of distance, where are the members of your group looking.

a. At a very close object

b. At an object within a few meters

c. Far off into the distance (infinity)

4. When you relax, part of the relaxation process is to relax the muscles in your eyes. The relaxed eye looks at objects at _________________.

The Near Point

Hold a pen or pencil, with writing on it, vertically at arms length.

1. Is the writing on the pen in focus?

2. Move the pen several inches inward. Is it still in focus?

The ability of the eye to focus on objects at different distances is called accommodation. The human eye has a rather remarkable ability to rapidly accommodate that exceeds any optical system designed by man.

3. Now slowly move the pen towards your eye. Is there a point at which your eye can no longer accommodate the pen? I.e., is there a point at which the writing on the pen starts to appears blurry?

4. Have each person locate this point as accurately as they can, and then measure the distance from their eye to the point (use units of cm.) If the group member wears glasses, have them make the determination without glasses. Note: the condition should be the writing on the pen becomes blurry, not that your eyes cross.

Fill out the table for your group.

Person	Distance (cm)

5. Find the average distance for the members of your group.

The closest point an object can be to your eye so that you can still accommodate it is called the near point. The near point distance, which is normally denoted by the letter N, varies significantly from person to person, and is very different for near-sighted versus far-sighted people. However, a typical value for adults with normal vision is around

N = 25 cm.

6. Did any of the members of your group have a value near 25 cm?

7. Did any of the members of your group have a value that varied significantly from 25 cm? Do these people wear glasses?

Angular Magnification

Have a member of your group hold a book across the room. Now walk the book slowly towards the other members of the group.

1. Does the apparent size of the book seem to change as it is brought nearer the group? If so how?

2. Did the book actually change size?

3. The figure below shows the book at two different positions with respect to the eye. Use a straight edge to draw rays from the front corners of the book to the vertex of the symbol for the eye.

4. Based on your answer to question 3, if the book didn't actually change size, what did change so that the book appears larger?

This idea is called angular magnification. Label the angle subtended by the nearer book as q' and the angle subtended by the more distant book as q. Label the distance from the book to the eye as d_n and d_f for the nearer and further book, respectively, and label the height of the book as h. The angular magnification is defined as

5. Find expressions for the tangents of q and q' in terms of the appropriate distances you've just labeled.

6. For small angles, if the angle is expressed in radians, tan q » q. This is called a small angle approximation. Use your answers to question 5 and the small angle approximation and find an expression for the angular magnification. Be sure to simplify to simplify completely the complex fraction you will obtain.

7. Angular magnification is a very simple idea. An object appears nearer because the ___________ it makes is larger than that made by the same object at a greater distance.

The Simple Magnifier

We can use a converging lens to enable us to magnify images. The figure below shows an object of height h at a distance N – the near point - from the eye.

8. Assuming the angle is small, find an expression for the angle q made by the object with the eye. (i.e. find tan θ and set tan θ ≈ θ)

9. When we use a simple magnifier with a relaxed eye, we place the object at the focal length of the lens. Where will the image be formed if the object is at the focal point of the lens?

The ray diagram below shows two rays from an object sitting at the focal point of a converging lens. Note all refracted rays will be parallel to the axis.

The angle q' is the angle that the observer will see the image making.

10. Find an expression for the angle q' assuming the angle is small. . (i.e. find tan θ and set tan θ ≈ θ)

11. The angular magnification of the image seen by the observer is M_q = q'/q. Find an expression for the angular magnification. Simplify the complex fraction completely.

Obtain lenses with 100 mm, 150 mm, and 250 mm focal lengths.

12. Predict if you use each lens each to look at a small object like a letter on a page which lens will make it seem bigger. Explain.

13. Use each lens as a magnifier with a relaxed eye (i.e. place the object at the focal point of the lens) and compare the magnification of the different objects. Do your observations agree with your prediction? Explain.

14. Assume the near point is 25 cm and determine the magnification for each of your lenses.

15. Can you use a diverging lens as a magnifier? Explain.

Obtain a -150 mm diverging lens and determine if you can magnify and image with it.

16. Did this agree with your prediction? Explain.