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 beam of light can converg

Question

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 beam of light can converge is _____ mm .

TestHub · Accepted Answer

For the refraction at the left surface, $u = - \infty, R = + 15 cm$ .

$\frac{μ_{2}}{v} - \frac{μ_{1}}{u} = \frac{μ_{2} - μ_{1}}{R}$

$\Rightarrow \frac{1.5}{v_{1}} - \frac{1}{- \infty} = \frac{1.5 - 1}{+ 15}$

$\Rightarrow v_{1} = 45 cm$

For the refraction at the right surface, $u = 45 - 30 = 15 cm, R = - 15 cm$

$\frac{μ_{2}}{v} - \frac{μ_{1}}{u} = \frac{μ_{2} - μ_{1}}{R}$

$\Rightarrow \frac{1}{v_{2}} - \frac{1.5}{15} = \frac{1 - 1.5}{- 15}$

$\Rightarrow v_{2} = 7.5 cm$

Therefore, the distance from the centre where the beam will converge is,

$15 + 7.5 = 22.5 cm = 225 mm$

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