Question 179 of 295

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

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Answer: 225

For the refraction at the left surface, $u=-\infty ,R=+15cm$.
$\dfrac{{\mu }_{2}}{v}-\dfrac{{\mu }_{1}}{u}=\dfrac{{\mu }_{2}-{\mu }_{1}}{R}$
$\Rightarrow \dfrac{1.5}{{v}_{1}}-\dfrac{1}{-\infty }=\dfrac{1.5-1}{+15}$
$\Rightarrow {v}_{1}=45cm$
For the refraction at the right surface, $u=45-30=15cm,R=-15cm$
$\dfrac{{\mu }_{2}}{v}-\dfrac{{\mu }_{1}}{u}=\dfrac{{\mu }_{2}-{\mu }_{1}}{R}$
$\Rightarrow \dfrac{1}{{v}_{2}}-\dfrac{1.5}{15}=\dfrac{1-1.5}{-15}$
$\Rightarrow {v}_{2}=7.5cm$
Therefore, the distance from the centre where the beam will converge is,
$15+7.5=22.5cm=225mm$