Question

A convex lens of focal length 10 cm is placed 30 cm in front of a second convex lens also 145 of the same focal length. A plane mirror is placed after the two lenses. Where should a point object be placed in front of the first lens so that it images on to itself? 

Answer 1

 The convex lenses and the plane mirror are shown in figure. The combination behaves like a concave mirror. Let the distance of the object from the first lens be x. 

For the ray to retrace its path it should be incident normally on the plane mirror. 

From the diagram we see that for lens L₂, 

From the lens equation we get

(1/v) – (1/u) = (1/f)  or 

u = -10 cm 

From the diagram we see that for lens L₁, 

v = 30-10 = 20 cm, f = +10cm, u =-x 

From the lens equation we get 

(1/v) – (1/u) = (1/f) or 

(1/20) – (1/-x) = (1/10) or 

x = 20 cm