A symmetric concave lens is made of material of refractive index n=1.50 and radi

Question

A symmetric concave lens is made of material of refractive index n=1.50 and radii of curvature |r|=20 cm.

a. What is the focal length of the lens?

b. An object 2.0 cm high is placed 40.0 cm in front of the lens. Use ray tracing to find the position and height of the image. To do this accurately, use a ruler or paper with a grid. Determine the image distance and image height by making measurements on your diagram.

c. Using equations, what is the image location?

d. Using equations, what is the image height? Use a negative value to indicate an inverted image.

Explanation / Answer

Part A)

The lens makers equation is

1/f = (n-1)(1/R1 - 1/R2) Since the lens is symmetric, R1 and R2 are the same value, but opposite in sign.

1/f = (1.5 -1)(1/-20 - 1/20)

f = -20 cm

Part B)

Can't do the accurate drawing and upload, just too much trouble with Cramster to upload photos, but I will calculate them for you. You can do your own drawings if you need them.

Part C)

Using 1/f = 1/p + 1/q, we have

1/-20 = 1/40 + 1/q

q = -13.3 cm

Part D)

Then, the magnifiction is found by M = -q/p

M = -(-13.3)/40 = .333 (positive magnification indicates upright image)

M = h'/h

.333 = h'/2

h' = .67 cm (upright)

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