Question

The distance between two identical concave mirrors of radius of curvature R is d. To coincide the image I on the object O itself, which is placed at the midpoint, can be

• A. R
• B. 2 R
• C. 3 R
• D. R/2

Answer 1

Answer: (A), (B)

R, 2R

Answer 2

For the image to coincide with the object, the light rays must retrace their path. This can occur in two primary ways:

1. Object at the center of curvature of both mirrors: If the object is at a distance R from each mirror (i.e., at their center of curvature), then $d/2 = R$, so $d=2R$. Light from the object hits the first mirror, forms an image at the object's position, which then acts as the object for the second mirror, again forming an image at the object's position.

2. Object at the focus of both mirrors: If the object is at a distance R/2 from each mirror (i.e., at their focus), then $d/2 = R/2$, so $d=R$. Light from the object hits the first mirror and becomes parallel. These parallel rays then hit the second mirror and converge at the object's position (since the object is at the focus of the second mirror as well).