Question

A square plate of side L is placed on the principal axis
at focal point Fof a convex mirror, such that the
principal axis is passes through the centre of plate
normally. The area of image of the plate is​

Answer 1

Answer:

The area of the image of the plate is  πr²/4

From given we have,

The distance of the object u = -f

The focal length of the convex lens = f

here, we use the mirror formula

• 1/v + 1/u = 1/f

• 1/v - 1/f = 1/f

• 1/v = 2/f

• v = f/2

Magnification, m = - v/u

m = - (f/2) / -f

m = 1/2

Thus, the new radius r of the circular plate will be magnified by magnification  amount for its image

The radius of the image will be

• r' = r * 1/2 = r/2

Thus, the area of the image of the plate will be

• A' = πr'² = π(r/2)² = πr²/4