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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.

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By Expert Faculty of Sri Chaitanya

The image is 300 cm below the lens.

The image is 56.25 below the lens.

The image is real.

The image is 30 cm below the lens.

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detailed solution

Correct option is A

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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