First slide

The lens

Question

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.

Moderate

A

The image is 300 cm below the lens
B

The image is 56.25 below the lens
C

The image is real
D

The image is 30 cm below the lens

Solution

For refraction through spherical surface, $μ_{1} = 1.2, μ_{2} = 1.5$
    $r = + 30 c m, u = - 40 c m$
    $∵ \frac{μ_{2}}{v} - \frac{μ_{1}}{u} = \frac{μ_{2} - μ_{1}}{t}$
            Or $\frac{1.5}{v} - \frac{1.2}{- 40} = \frac{1.5 - 1.2}{30} o r \frac{1.5}{v} + \frac{12}{400} = \frac{3}{300}$
            Or $\frac{1.5}{v} = \frac{1}{100} - \frac{3}{100} = \frac{- 2}{100}$
            Or $v = \frac{- 100}{2} \times 1.5 = - 75 c m$
            For refraction through spherical surface, $μ_{1}^{'} = 1.5, μ_{2}^{'} = 1, u' = - 75 c m, t' = - 30$
                 $∴ \frac{μ_{2}^{'}}{v'} - \frac{μ_{1}^{'}}{u'} = \frac{μ_{2}^{'} - μ_{1}^{'}}{t}$
            Or $\frac{1}{v'} + \frac{1.5}{75} = \frac{1 - 1.5}{- 30}$
             $∴ v' = - 300 c m$

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