Optics 7 Question 35
36. $A B$ and $C D$ are two slabs. The medium between the slabs has refractive index 2. Find the minimum angle of incidence of $Q$, so that the ray is totally reflected by both the slabs.
$(2005,2 M)$
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Solution:
- Critical angles at 1 and 2
$$ \begin{aligned} & \theta _{C _1}=\sin ^{-1} \frac{\mu _1}{\mu _2}=\sin ^{-1} \frac{1}{\sqrt{2}}=45^{\circ} \\ & \theta _{C _2}=\sin ^{-1} \frac{\mu _3}{\mu _2}=\sin ^{-1} \frac{\sqrt{3}}{2}=60^{\circ} \end{aligned} $$
Therefore, minimum angle of incidence for total internal reflection to take place on both slabs should be $60^{\circ}$.
$$ i _{\text {min }}=60^{\circ} $$
