Question

Half part of a convex glass lens L (μ =3/2) of radius of curvature 40 cm is silvered at right side. A plane mirror M and an object O is placed ⏊ to the principle axis, as shown at the indicated positions. Image formed by silvered lens and plane mirror has no parallel x but size of image formed by silvered is one third of that formed by plane mirror. Find the distance of plane mirror a & silvered lens b from the object. 

(a) a = 40/3 cm & b = 20 cm 

(b) a = 20 cm & b = 40/3 cm 

(c) a = 20/3 cm & b = 20 cm 

(d) a = 40/3 cm & b = 10 cm

Answer 1

From the problem 9(d) F_L = R/2(2μ-1) = 40/2[2(3/2)-1] = 10 cm (+convex) 

It is given in problem image formed by silvered lens & plane mirror has no parallel but size of image formed by silvered is (1/3) of that formed by plane mirror. So image 

formed by both mirrors coincide.