Question

A circular plate of radius r is placed on the principal axis at distance f from a convex mirror of focal length f, such that the principal axis is passes through the centre of plate normally. The area of image of the plate is

Answer 1

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