Question

A double convex lens is made of glass with a refractive index of 1.5. If its focal length is 30 cm, then the radius of curvature of each of its curved surfaces is:

(a) 30 cm
(b) 45 cm
(c) 60 cm
(d) 90 cm

Answer 1

The radius of curvature of each of the curved surfaces of a double convex lens with a refractive index of 1.5 and a focal length of 30 cm is 60 cm.

Step-by-step explanation:

In order to find the radius of curvature of each curved surface of a double convex lens, we can use the Lens Maker's Equation:

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

Where f is the focal length, n is the refractive index of the lens material, and R1 and R2 are the radii of curvature of the two surfaces.

Given that the refractive index of the glass is 1.5 and the focal length is 30 cm, we can rearrange the equation to solve for the radii of curvature, R1 and R2:

R1 = R2 = 2f/(n-1)

Substituting the values, we have:

R1 = R2 = 2 * 30 cm / (1.5 - 1) = 2 * 30 cm / 0.5 = 60 cm

Therefore, the correct option is (c) 60 cm.