Question

Two spherical mirrors, one convex and the other concave, each of same radius of curvature R are arranged coaxially at a distance of 2R from each other. A small circle of radius a is drawn on the convex mirror as shown in figure. What is the radii of first two images of the circle

Answer 1

(i)  hi = a/3

(ii)  hi = a/11

Explanation:

We know the mirror equation:

1/v + 1/u = 1/f

For the first reflection:

1/v - 1/2r = -2/r

1/v = -2/r + 1/2r

 1/v = -2r/3

m = -v/u = hi/ho = 2r / (3r/2) = hi/a

hi = a/3 -------(1)

For the convex mirror:

u = 2r -2r/3 = 4r/3

1/v + 1/u = 1/f

1/v - 3/4r = 2/r

1/v = 11/ur

v = ur/11

m = v/u = 4r*3 / 11*4r = 3/11 = hi/ (a/3)

hi = a/11  -------(2)