The radius of curvature of each surface of a convex lens having refractive index 1 . 8 is 20 cm . The lens is now immersed in a liquid of refractive index 1 . 5 . The ratio of power of lens in air to

Question

The radius of curvature of each surface of a convex lens having refractive index 1 . 8 is 20 cm . The lens is now immersed in a liquid of refractive index 1 . 5 . The ratio of power of lens in air to its power in the liquid will be x : 1 . The value of x is

TestHub · Accepted Answer

The power of a lens is given by P 1 = 1 f Using Lens Maker's formula, P 1 = ( 1 .8 − 1 ) 1 R 1 − 1 R 2 and P 2 = 1 f immersed = 1 .8 1 .5 − 1 1 R 1 − 1 R 2 Hence, the ratio is, P 1 P 2 = ( 1 .8 − 1 ) 1 .8 1 .5 − 1 = 0 .8 × 1 .5 0 .3 = 4

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