A thin biconvex lens is prepared from the glass ( =1.5 ) both curved surfaces of which have equal radii of 20 cm each. Left side surface of the lens is silvered from outside to make it reflecting. To have the position of image and object at the same place, the object should be placed, from the lens at a distance of ________ cm.

Step-by-step solution

When one surface of a lens is silvered, the system behaves like an equivalent mirror. The light refracts through the lens, reflects off the silvered surface, and refracts through the lens again, so the equivalent power is: P_ eq = P_L + P_M + P_L = 2P_L + P_M Power of the biconvex lens: For a thin biconvex lens with R₁ = +20 cm , R₂ = -20 cm and = 1.5 , the lens maker's formula gives: 1 f_L = ( - 1) ( 1 R₁ - 1 R₂ ) 1 f_L = (1.5 - 1) ( 1 20 - 1 -20 ) = 0.5 2 20 = 1 20 cm ⁻¹ So, P_L = 1 20 cm ⁻¹ . Power of the silver