A ray of light passing through a prism ( =3) suffers minimum devi… - Vidyadip

MCQ

A ray of light passing through a prism $(\mu=\sqrt{3})$ suffers minimum deviation. It is found that the angle of incidence is double the angle of refraction within the prism. Then, the angle of prism is ..... . (in degrees)

A
$50$
B
$80$
C
$30$
✓
$60$

✓

Answer

Correct option: D.

$60$

d
At minimum deviation $r_{1}=r_{2}=\frac{A}{2}$

Also given ${i}=2 {r}_{1}={A}$

Now $1 \sin i =\sqrt{3} \sin r_{1}$

$1 \sin A=\sqrt{3} \sin \frac{A}{2}$

$2 \sin \frac{A}{2} \cos \frac{A}{2}=\sqrt{3} \sin \frac{A}{2}$

$\cos \frac{A}{2}=\frac{\sqrt{3}}{2} \Rightarrow \frac{A}{2}=30^{\circ}$

$A=60^{\circ}$

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