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  4. 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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Q. 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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Solution:

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$\frac{\frac{3}{2}}{ V }-\frac{1}{\infty}=\frac{\frac{3}{2}-1}{15}$
$\frac{3}{2 V }=\frac{1}{30}$
$V =45 \,cm$
$\frac{1}{ V }-\frac{3}{\frac{2}{15}}=\frac{1-\frac{3}{2}}{\frac{2}{-15}}$
$\frac{1}{ V }-\frac{1}{10}=\frac{1}{30}$
$\frac{1}{ V }=\frac{1}{10}+\frac{1}{30}=\frac{4}{30}$
$V =7.5$
$V =22.5$
$V =225 \,mm$