Question

A plano-convex lens of focal length 20 cm has its plane side silvered:

A. The radius of curvature of curved surface of plano-convex lens is equal to half of radius of curvature of a surface of equi-convex lens of focal length 20 cm
B. A object placed at15 cm on the axis on the convex side of silvered plano-convex lens gives rise to an image at a distance of 30 cm from it
C. An object placed at a distance of 20 cm on the axis on the convex side of silvered plano-convex lens gives rise to an image at 40 cm from it
D. Silvered plano-convex lens acts as a concave mirror of focal length 10 cm

Answer 1

A plano-convex lens of focal length 20 cm has its plane side silvered and behaves as a converging lens. The radius of curvature of the curved surface of the plano-convex lens is equal to the radius of curvature of the surface of an equi-convex lens with the same focal length. An object placed at a distance of 15 cm on the axis of the convex side of the silvered plano-convex lens gives rise to an image at a distance of 30 cm from it. An object placed at a distance of 20 cm on the axis of the convex side of the silvered plano-convex lens gives rise to an image at 40 cm from it. The silvered plano-convex lens does not act as a concave mirror.

Step-by-step explanation:

In this question, we are dealing with a plano-convex lens. A plano-convex lens has one flat surface (called the plane side) and one curved surface (called the convex side). The focal length of the lens is given as 20 cm.

A. The radius of curvature of the curved surface of a plano-convex lens is equal to the radius of curvature of the surface of an equi-convex lens with the same focal length. In this case, the focal length is 20 cm, so the radius of curvature of the curved surface is also 20 cm.

B. To find the location of the image for an object placed at a distance of 15 cm on the axis of the convex side of the silvered plano-convex lens, we can use the lens formula:

1/f = 1/v - 1/u

Where f is the focal length, v is the image distance, and u is the object distance

Substituting the given values, we get:

1/20 = 1/30 - 1/15

Solving this equation, we find that v = 30 cm, which matches the given value.

C. Following the same approach as in part B, for an object placed at a distance of 20 cm on the axis of the convex side of the silvered plano-convex lens, we can calculate the image distance:

1/f = 1/v - 1/u

Substituting the given values, we get:

1/20 = 1/40 - 1/20

Solving this equation, we find that v = 40 cm, which matches the given value.

D. The silvered plano-convex lens does not act as a concave mirror. It still functions as a converging lens, with a focal length of 20 cm.