Question

A symmetric double convex lens with a focal length of 28.0 cmcm is to be made from glass with an index of refraction of 1.51.

Part A What should be the radius of curvature for each surface? Express your answer to two significant figures and include the appropriate units.

Answer 1

Use the lens maker's formula:

1/f=(n-1) [(1/R1)-(1/R2)]

Given,

focal length.(f=28 cm =0.28 m given).

n is refractive index of material of lens relative to surrounding medium. (n=1.51 given).

R1 is radius of curvature of first surface.

R2 is radius of curvature of second surface

R1=R2=R given.R1 is positive and R2 is

negative in Cartesian sign convention.

Then,

(1/f)=(1.51-1)(2/R). Or

(1/0.28)=(0.51)(2/R)=1.02/R.

Therefore,

R=(1.02)(0.28)m=0.2856 m ~=28.56 cm.

​​​​Hence,R=28.56 cm

or R= 0.2856 m (answer)