A parallel beam of light is allowed to fall on a transparent spherical globe of diameter 30 cm and refractive index 1.5. The distance from the centre of the globe at which the beam of light can converge is_________mm.

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answer is 225.

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Detailed Solution

$\begin{array}{l} \frac{\frac{3}{2}}{V} - \frac{1}{\infty} = \frac{\frac{3}{2} - 1}{15} \\ \frac{3}{2 V} = \frac{1}{30} \\ V = 45 cm \end{array}$
$\begin{array}{l} \frac{1}{V} - \frac{3}{\frac{2}{15}} = \frac{1 - \frac{3}{2}}{\frac{2}{- 15}} \\ \frac{1}{V} - \frac{1}{10} = \frac{1}{30} \\ \frac{1}{V} = \frac{1}{10} + \frac{1}{30} = \frac{4}{30} \\ V = 7 .5 \\ Distance from center = 15 + 7.5 = 22 .5 cm = 225 mm \end{array}$

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