First slide

Ray optics

Question

A 4 $\sqrt{3}$ cm diameter beam of light is incident on the surface of a transparent sphere of radius $4 cm$ as shown in figure. If the beam converges at point B as shown in figure, the refractive index of the material of the sphere is

Moderate

A

1.5
B

$2 / \sqrt{3}$
C

$\sqrt{3}$
D

$\sqrt{\frac{3}{2}}$

Solution

In $ΔPOB$ , $r + r = i \Rightarrow r = \frac{i}{2}$
In $ΔPOQ, \frac{PQ}{OP} = \sin i$
$\begin{array}{l} \Rightarrow sini = \frac{\sqrt{3}}{2} \\ \Rightarrow i = 60^{o} \end{array}$
By snell's law, $\sin i = μ \sin r$
$\Rightarrow μ = \frac{\sin i}{\sin i / 2} = 2 \cos \frac{i}{2} = 2 \cos 30^{o}$
$\Rightarrow μ = \sqrt{3}$

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