A Plano-convex Lens Acts Like A Concave Mirror Of 28 Cm Focal Length When Its Plane Surface Is Silvered And Like A Concave Mirror Of 10 Cm Focal Length When Its Curved Surface Is Silvered. What Is The Refractive Index Of The Material Of The Lens?  

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Question

A plano-convex lens acts like a concave mirror of 28 cm focal length when its plane surface is silvered and like a concave mirror of 10 cm focal length when its curved surface is silvered. What is the refractive index of the material of the lens?  

Solution

Correct option is

1.55

 

In the first case we have               (∵ fm = ∞) 

                   

In the second case we have

                   

Where fm is the focal length of the curved silvered surface. Hence fm = R/2 where R is the radius of curvature of the curved surface.

Subtracting (i) and (ii) we get

                    

  

From (i) we have f1 = 28 × 2 = 56 cm. Now   

            

  

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