THE EXPERIMENT

Apparatus

optical bench, with light source, screen, and 3 lens holders
convex and concave lenses.
ruler.
laser and marker board

A. MEASUREMENTS OF f AND VERIFICATION OF THE LENS EQUATION

Take one of the convergent lenses, L₁, and mount it in a lens holder. Mount the screen at the end of the optical bench directly above the 98 cm ruling. Now take a distant object (u = ) (window frame, distant lamp, etc.), line up the lens and screen with the object and slide the lens until the sharpest possible image is produced on the screen. Record f₁ (f₁ = v, distance from lens to screen) and P₁, including an error estimate. Record whether the image is erect or inverted, real or virtual. Repeat with the second converging lens, L₂. Next, use L₁ and L₂, next to each other, placed as close together as you can and determine the focal length f₁₂ and power P₁₂ of the combination, reckoning distance from the midpoint of the lenses. Compare with Eq. (6).

Next, take the concave lens, L₃, and verify that, by itself it cannot produce a real image of a distant object. Now combine it with the stronger convex lens, and measure the focal length f and power P of the combination. Deduce f₃ and P₃ of the concave lens.

Place the filament in the light source 80 cm beyond the end of the optical bench and in line with the optical bench. Put the stronger convergent lens at the 10 cm mark (now u = object distance is 90 cm). Measure, using the screen, the image distance. Repeat with the lens at the 20, 30, and 40 cm marks. Tabulate u, v, u^-1, v^-1 and (u^-1 + v^-1) to verify Eq. (1). Include an estimate of the errors in each step.

B. THE EYE AS VARIABLE LENS AND SCREEN

In this section experiments will be done in which the eye acts as a lens, L, of variable focal length. At the same time the retina acts as a screen at a fixed distance v = D behind L. The far and near points of the eye and their modification by lenses will be studied. (use D = 2.4 cm)

Far Point - Assume that for your relaxed eye (with glasses or contact lenses, if you wear them), the far point is u_far = infinity.

Now calculate the new far point, u_far, that you would have with the stronger convergent lens next to your eye.

Now measure the new far point. Put the stronger convergent lens close to your eye and, holding the bench screen in your hand as object, measure the distance of the new far point, u_far, the maximum distance of sharp vision. (Approximate the distance with a ruler from the bridge of your nose and allow 2.0 cm for the recess of L.) Compare the observed and measured values and comment on your results. Would you expect u_farto be equal to the focal length of the converging lens?

Hint:

Remember f_eye = 2.4 cm for the relaxed eye, you have already measured the focal length of the convergent lens, (f_lens). Use the relation
= + .

Then use v = 2.4 cm with f_combination to calculate the new far point.

Near Point - Using the bench screen as object, measure approximately the distance u_near of the near point where you can still just manage to focus clearly on the scale (with glasses or contact lenses, if you wear them). Using v = 2.4 cm calculate f^min from u_near, and P^max from f^min. Assuming that your far point is u_{far =}, calculate the accommodating power of your eye in diopters:

P^acc = P^max - P^min .

(7)

Values of the Accommodative Power at Ages from 8 to 68 (Duane 1912) Measure in diopters.

  Age      Mean Value      Usual Upper Limit     
   8          13.8                15.4           
   12         13.1                14.7           
   16         12.4                13.9           
   20         11.5                13.0           
   25         10.2                11.8           
   30          8.9                10.4           
   35          7.3                8.9            
   40          5.9                7.2            
   50          2.0                3.0            
  60+          1.1                1.5

Table 1

Compare the value for the accommodative power for your eye with the table. Would you expect college students to have more or less accommodative power than truck drivers?

C. THE BLIND SPOT

In this experiment the blind spot of one student (the "subject") will be mapped out by his partner. Abnormally shaped blind spots occur in glaucoma patients. Additional blind spots (scars) can be created by excessive exposure to the sun or other strong light sources such as welding arcs.

The subject sits down 200 cm from a blackboard and covers his left eye. His partner draws a small asterisk directly in front of the subject's right eye. The subject must now focus firmly and persistently on the asterisk. His partner very slowly moves a laser spot along the blackboard, starting from the asterisk and moving horizontally to the subject's right.

At a certain point the light will become invisible to the subject, further on again visible. Both points should be marked on the board (see Fig. 7). Starting from the midpoint P between theses two points, the partner now moves the laser spot in various directions and marks the points of reappearance. Thus, a map of the blind spot is produced on the board.

Figure 7 Mapping the Blind Spot

Record the dimensions and shape of the blind spot on the board and its position relative to the asterisk. Make a scale drawing in your report.

Using Eq. (2), the known distance of the object, u = 200 cm, and the known distance of the retinal image, v = D = 2.4 cm, calculate the actual distance from the fovea to the blind spot on the retina, and the actual vertical and horizontal diameters of the blind spot. (The eye automatically forms the image of the point of fixation [the asterisk] on the fovea.) This calculation is an approximation which ignores effects caused by the medium in the eye not being air (it is called vitreous humor and has a refractive index similar to water). This modifies the results slightly - your calculations will overestimate the real values by about 20%.