A diverging lens is fabricated from a piece of glass with an index of refraction of 1.5.It is ground such that one surface of the lens is convex and the other surface is concave.The convex surface is part of a sphere with a radius of 45 cm and the concave surface is part of a sphere with a radius of 20 cm.What is the power of this lens in diopters?
A)-1.4 D
B)-1.5 D
C)-1.8 D
D)-3.2 D
E)-3.5 D

Question

Quizplus · Accepted Answer

The power of a lens is given by the equation:P = 1/fwhere f is the focal length of the lens.For a diverging lens, the focal length is negative. The focal length of a lens can be calculated using the lensmaker's equation:1/f = (n-1) * (1/R1 - 1/R2)where n is the index of refraction of the lens, R1 is the radius of curvature of the first surface, and R2 is the radius of curvature of the second surface.In this case, the index of refraction of the lens is 1.5, the radius of curvature of the first surface is 45 cm, and the radius of curvature of the second surface is 20 cm. Substituting these values into the lensmaker's equation, we get:1/f = (1.5-1) * (1/45 cm - 1/20 cm)1/f = -0.033 cm^-1f = -30 cmTherefore, the power of the lens is:P = 1/f = -1/30 cm = -3.33 DThe closest answer choice is -3.2 D, so the correct answer is A.

A Diverging Lens Is Fabricated from a Piece of Glass