First slide

Ray optics

Question

A ray of light incident on one refracting face of a prism of angle $75^{0}$ . It undergoes total internal reflection at the second face. If $μ = \sqrt{2}$ , the maximum angle of incidence on the first face is

Moderate

A

$45^{0}$
B

$30^{0}$
C

$60^{0}$
D

$90^{0}$

Solution

$\begin{array}{rcl} minimum value of r_{2} & = & i_{c} is 45^{0} as μ = \sqrt{2} \\ then r_{1} & = & A - r_{2} will be 75^{0} - 45^{0} = 30^{0} \\ according to Snell' s law \frac{{sini}_{1}}{{sinr}_{1}} & = & \sqrt{2} \\ {sini}_{1} & = & \sqrt{2} \sin 30^{0} = \frac{1}{\sqrt{2}} \\ i_{1} & = & 45^{0} \end{array}$

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