Question

A convex lens of focal length 15 cm is placed coaxially in front of a convex mirror. The lens is 5 cm from the pole of the mirror. When an object is placed on the axis at a distance of 20 cm from the lens, it is found that the image coincides with the object. Calculate the radius of curvature of the mirror - (consider all-optical event): 

Options

• 45 cm

• 55 cm

• 65 cm

• 85 cm

Answer 1

55 cm

Explanation:

f = 15 cm

I₁ is the image formed by a convex lens in the absence of a convex mirror. Because the mirror is 5 cm away from the lens, I₁ is 60 - 5 = 55 cm away from the convex mirror. Now, the final image I₂ is formed at O, which means that rays incident on the mirror after reflection are incident on the mirror normally. As a result, I₁ is the centre of curvature. As a result, R₁ = 55 cm.