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 focal length of this lens?
A)-72 cm
B)-9.2 cm
C)-28 cm
D)-17 cm
E)-64 cm

Question

Quizplus · Accepted Answer

The focal length of a diverging lens is negative. The focal length of a lens is given by the equation:1/f = (n-1) * (1/R1 - 1/R2)where:f is the focal lengthn is the index of refraction of the lensR1 is the radius of curvature of the first surfaceR2 is the radius of curvature of the second surfaceIn this case, the index of refraction 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 equation, we get:1/f = (1.5-1) * (1/45 cm - 1/20 cm)1/f = 0.5 * (-1/45 cm + 1/20 cm)1/f = -0.5 * (1/90 cm)f = -90 cmTherefore, the focal length of the lens is -90 cm, which is choice A.

A Diverging Lens Is Fabricated from a Piece of Glass