The radius of curvature of the curved surface of a plano-convex lens is 20 cm. If the refractive index of the material of the lens be 1.5, then focal length of lens will be:

Concept:

• For a plano-convex lens, one of the surfaces is flat (Plano) and the other is curved (convex).
• The radius of curvature of the curved surface is given as 20 cm, and the refractive index of the material of the lens is 1.5.
• The focal length of the lens can be calculated using the lens maker's formula:

1/f = (n - 1) × (1/R1 - 1/R2)

where

f is the focal length of the lens,

n is the refractive index of the lens material,

R1 is the radius of curvature of the first surface (the flat surface in this case, which is infinite), and

R2 is the radius of curvature of the second surface (the curved surface in this case).

Since the first surface is flat, the radius of curvature R1 is infinite, and the term (1/R1) becomes zero. Therefore, the lens maker's formula simplifies to:

1/f = (n - 1) ×  (1/R2)------(1)

Calculation:

Substituting the values in equation (1), we get:

1/f = (1.5 - 1) × (1/20)

1/f = 0.025

f = 1/0.025

f = 40 cm

Therefore, the focal length of the plano-convex lens is 40 cm.

The correct answer is option (4)