A thin equiconvex lens is placed on a plane mirror as shown in figure. A point object O is placed on the principal axis of the lens at a distance of $$20$$ cm from the lens. It is observed that after refraction through the lens, reflection at the mirror and again refraction through the lens, the final image coincides with the object. If radius of curvature of the curved surfaces of the lens is $$20$$ cm, refractive index of its material is

Question

Infinity Learn · Accepted Answer

In this case rays of light after refraction through the lens must become parallel to the principal axis and strike the mirror normally. So the object must be at the first focal point of the lens. Therefore f $$=$$ focal length $$=$$ $$20$$ cmNow $$2($$μ−$$1)R=1f$$⇒μ$$=1+R2f=1+202$$×$$20=1.5$$

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