At the mouth of a cylindrical vessel, a convex lens of refractive index 1.5 and radius of curvature of curved surface 30 cm is filled. A point source S is at the bottom of vessel. The height of vessel is 40 cm and filled with liquid of refractive index 1.2. Find the position of image.

Question

Infinity Learn · Accepted Answer

For refraction through spherical surface, $μ_{1} = 1 .2, μ_{2} = 1 .5$

$r = + 30 cm, u = - 40 cm$

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

Or, $\frac{1.5}{v} - \frac{1.2}{- 40} = \frac{1.5 - 1.2}{30} \Rightarrow \frac{1.5}{v} + \frac{12}{400} = \frac{3}{300}$

Or, $\frac{1.5}{v} = \frac{1}{100} - \frac{3}{100} = \frac{- 2}{100}$

Or, $v = \frac{- 100}{2} \times 1.5 = - 75 cm$

For refraction through spherical surface, $μ_{1}^{'} = 1.5, μ_{2}^{'} = 1, u' = - 75 cm, r' = - 30$

$∴ \frac{μ_{2}^{'}}{v'} - \frac{μ_{1}^{'}}{u'} = \frac{μ_{2}^{'} - μ_{1}^{'}}{r'}$

Or, $\frac{1}{v'} + \frac{1.5}{75} = \frac{1 - 1.5}{- 30}$

$∴ v' = - 300 cm$

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