Find the focal length of a double concave lens made of glass (n=1.52), having radii of curvature of 6.5 cm and 7.5 cm.

Answer 1

The thickness of the lens is not given, so assume it is a thin lens.

Using the thin-lens approximation of the lens-maker's formula,
P=1/f=(n-1)(1/R1-1/R2)
where
n=refractive index of lens material in air
R1, R2 are radii of curvature of lens surfaces, using the convention that R>0 for convex, R<0 for concave, and R=0 for flat surface. Sign of back surface is reversed. (front surface faces light source).

Applying equation,
n=1.52, R1=-6.5, R2=-(-7.5)
P=1/f=(1.52-1)(-1/6.5-1/7.5)
=-0.1493
The focal length is thus the reciprocal of P.