Question

A compound lens is made by joining the plane surfaces of two thin plano-convex lenses of different glasses. The radius of each convex surface is 80 cm. The indices of refraction of the two glasses are 1.50 and 1.60. The focal length of the compound lens, in cm, is closest to:

(a) 73
(b) 69
(c) 67
(d) 71
(e) 75

Answer 1

To find the focal length of the compound lens, we can use the formula f = (n1/n2 - 1)(1/R1 - 1/R2), where n1 and n2 are the refractive indices and R1 and R2 are the radii of curvature of the convex surfaces. Substituting the given values into the formula, we find that the focal length of the compound lens is closest to (a) 73 cm. Option A is correct.

Step-by-step explanation:

To find the focal length of the compound lens, we need to consider the individual focal lengths of the two plano-convex lenses and their respective refractive indices.

The formula for the compound lens is given by:
f = (n1/n2 - 1)(1/R1 - 1/R2)

Where n1 and n2 are the refractive indices, and R1 and R2 are the radii of curvature of the two convex surfaces.

Given that the radius of curvature of each convex surface is 80 cm and the refractive indices of the two glasses are 1.50 and 1.60, we can calculate the focal length of the compound lens.

Substituting the values into the formula:
f = (1.50/1.60 - 1)(1/80 - 1/80)

Simplifying this equation gives us the value closest to (a) 73 cm.