For the given incident ray as shown in the figure, the condition of...

For the given incident ray as shown in the figure, the condition of the total internal reflection of this ray and the minimum refractive index of prism will be:

Options

A $\frac{\sqrt{3}+1}{2}$
B $\frac{\sqrt{2}+1}{2}$
C $\sqrt{\frac{3}{2}}$
D $\sqrt{\frac{7}{6}}$

Correct answer

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

Step-by-step solution

For given condition and use snell's law 1.

\sin 45^{\circ}=\mu \sin \left(90-q_C\right)

\begin{array}{ll} \frac{1}{\sqrt{2}}=\mu \cos \theta_C=\sqrt{\mu^2-1} \\ \Rightarrow \quad \mu^2=1+\frac{1}{2}=\frac{3}{2} \\ \Rightarrow \quad \mu=\sqrt{\frac{3}{2}} \end{array}

<img src="https://cdn-question-pool.Quantrex.app/pyq/neet/T6pB9utHm1G6RrdAGfag68UtmfFyqrc3KQqvg7x0D58.original.fullsize.png">

\begin{array}{ll} \therefore & \sin \theta_c=\frac{1}{\mu} \\ \Rightarrow \quad \cos \theta_c=\sqrt{\frac{\mu^2-1}{\mu}} \end{array}

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