The angle of incidence for a ray of light at a refracting surface...

The angle of incidence for a ray of light at a refracting surface of a prism is

{45}^{o}

. The angle of prism is

{60}^{o}

. If the ray suffers minimum deviation through the prism, the angle of minimum deviation and refractive index of the material of the prism respectively, are:

Options

A ${45}^{o}; \dfrac{1}{\sqrt{2}}$
B ${30}^{o}; \sqrt{2}$
C ${45}^{o}; \sqrt{2}$
D ${30}^{o}; \dfrac{1}{\sqrt{2}}$

Correct answer

B. ${30}^{o}; \sqrt{2}$

Step-by-step solution

At minimum deviation

{\delta}_\min = 2i - A

{\delta}_\min = 2\left(45\right) - 60

{\delta}_\min = {30}^{o}

Refractive index of material is

\mu = \dfrac{\sin \left(\dfrac{{\delta}_{\text{ min }} + A}{2}\right)}

{sin

\left(\dfrac{A}{2}\right)} = \dfrac{\sin \left(\dfrac{30 + 60}{2}\right)}{\sin \left({30}^{o}\right)}

\mu = \dfrac{sin {45}^{o}}{sin {30}^{o}} = \dfrac{\dfrac{1}{\sqrt{2}}}{\dfrac{1}{2}} = \sqrt{2}

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