For a diverging lens with one flat surface,the radius of curvature for the curved surface is 27.0 cm.What must the index of refraction be so that the focal length is -15.0 cm?

Question

Quizplus · Accepted Answer

Using the lens maker's formula:
1/f = (n-1)((1/R1)-(1/R2))
where n is the index of refraction, R1 is the radius of curvature of one side, R2 is the radius of curvature of the other side, and f is the focal length.

If one surface is flat, R1 is infinity. Thus:
1/f = (n-1)(-1/R2)
-1/R2 = 1/f(n-1)
R2 = -f(n-1)

Plugging in the given values:
-15 = -27(n-1)/(n-1)
-15(n-1) = -27
n-1 = 27/15
n-1 = 1.8
n = 2.8

Therefore, the answer is choice C.

For a Diverging Lens with One Flat Surface,the Radius of Curvature