Two transparent media having refractive indices 1.0 and 1.5 are separated by a spherical refracting surface of radius of curvature 30 cm. [2023]

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Solution

Q.
Two transparent media having refractive indices 1.0 and 1.5 are separated by a spherical refracting surface of radius of curvature 30 cm. The centre of curvature of surface is towards denser medium and a point object is placed on the principal axis in rarer medium at a distance of 15 cm from the pole of the surface. The distance of image from the pole of the surface is ________cm. [2023]

Ans.
(30)

$\frac{μ_{2}}{v} - \frac{μ_{1}}{u} = \frac{μ_{2} - μ_{1}}{R}$

$\frac{1.5}{v} - \frac{1}{- 15} = \frac{1.5 - 1}{30} = \frac{1}{60}$

$\frac{1.5}{v} + \frac{1}{15} = \frac{1}{60}$

$\frac{1.5}{v} = \frac{1}{60} - \frac{1}{15} = \frac{- 1}{20}$

$\frac{1.5}{v} = - \frac{1}{20} \Rightarrow v = - 30 cm$

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