Question

Focal length of a plano convex lens when refractive index is given

Answer 1

Answer:

The lens maker’s equation is

1f=(μ−1)(1R1+1R2), where,

f is the focal length of the lens,

μ is the refractive index of the material of the lens,

R1 is the radius of curvature of the surface closer to the object, and,

R2 is the radius of curvature of the surface farther away from the object.

The sign convention used is that R1 is positive for a convex lens and negative for a concave lens and R2 is negative for a convex lens and positive for a concave lens.

In the given case, R1=R2 and μ=n.

Since the second surface of the lens is plane, R2=∞⇒1R2=0.

⇒1f=(n−1)(1R+0)=n−1R.

⇒f=Rn−1.