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  • A ray of light when falls on a liquid – air interface at angle <img alt="\mathrm{45^{\circ}}" sr

A ray of light when falls on a liquid \mathrm{A}– air interface at angle \mathrm{45^{\circ}}, it just gets total reflection. When a ray of light falls on liquid \mathrm{B} – air interface at angle \mathrm{30^{\circ}}, it does not emerge out. We can infer that:

Option: 1

\mathrm{\mu_A>\mu_B}


Option: 2

\mathrm{\mu_A<\mu_B}


Option: 3

\mathrm{\mu_{\mathrm{A}}=\mu_{\mathrm{B}}}


Option: 4

can’t be inferred


Answers (1)

For liquid \mathrm{A}– air interface,
\mathrm{\mu_{\mathrm{A}}=\frac{1}{\sin \mathrm{i}_{\mathrm{c}}}=\frac{1}{\sin 45^{\circ}}=\sqrt{2}}
For liquid \mathrm{B} – air interface, the ray does not emerge out for \mathrm{\theta=30^{\circ} \text {, i.e., } i_c \leq 30^{\circ}}
\sin \mathrm{i}_{\mathrm{c}} \leq 30^{\circ}=\frac{1}{2} \quad \text { or } \quad \frac{1}{\sin \mathrm{i}_{\mathrm{c}}} \geq 2 \Rightarrow \mu_{\mathrm{B}} \geq 2

Posted by

Sumit Saini

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