Question

An equilateral prism is made of a material of refractive index$\sqrt{3}$.The angle of minimum deviation for the prism is

• A. ${90}^o$
• B. ${60}^o$
• C. ${45}^o$
• D. ${30}^o$

Answer 1

Answer: (B)

${60}^o$

$A={60}^o$
$\mu =\frac{sin\left(\frac{A+{\delta }_m}{2}\right)}{\frac{sinA}{2}}\Rightarrow \sqrt{3}=\frac{sin\left(\frac{{60}^o+{\delta }_m}{2}\right)}{sin{30}^o}$
$sin\left(\frac{{60}^o+{\delta }_m}{2}\right)=\sqrt{3}\times \frac{1}{2}=\frac{\sqrt{3}}{2}=sin{60}^o$
${60}^o+{\delta }_m={120}^o-\Rightarrow {\delta }_m={120}^o-{60}^o={60}^o$