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A thin convex lens made of glass of refractive index 1.5 has a focal length f in air. When it is completely immersed in a certain transparent liquid, its focal length becomes 2f . If the refractive index of the liquid is x 5 , the value of x is

Correct answer

6

Step-by-step solution

Let the radii of curvature of the lens surfaces be R₁ and R₂ . Using the Lens Maker's formula for the lens in air: 1 f = ( _g - 1) ( 1 R₁ - 1 R₂ ) 1 f = (1.5 - 1) ( 1 R₁ - 1 R₂ ) = 0.5 ( 1 R₁ - 1 R₂ ) When the lens is immersed in the liquid of refractive index _l , the new focal length is 2f . Using the Lens Maker's formula again: 1 2f = ( _g _l - 1 ) ( 1 R₁ - 1 R₂ ) 1 2f = ( 1.5 _l - 1 ) ( 1 R₁ - 1 R₂ ) Dividing the first equation by the second equation, we get: 2f f = 0.5 1.5 _l - 1 2 = 0.5 1.5 _l - 1 1.5 _l - 1

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