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  • If a ray of light in a denser medium strikes a rarer medium at an angle of incidence  , the angle

If a ray of light in a denser medium strikes a rarer medium at an angle of incidence \mathrm{i} , the angles of reflection and refraction are respectively, \mathrm{r} and \mathrm{r'} . If the reflected and refraction rays are at right angles to each other, the critical angle for the given pair of media is:

Option: 1

\mathrm{sin^{-1}(tan\ r')}


Option: 2

\mathrm{sin^{-1}(tan\ r)}


Option: 3

\mathrm{sin^{-1}(tan\ i)}


Option: 4

\mathrm{cot^{-1}(tan\ i)}


Answers (1)

best_answer

We know that, \frac{1}{\mu}=\frac{\sin i}{\sin r^{\prime}}
\begin{aligned} & \text { But } \quad r+r^{\prime}=90^{\circ} \quad \text { or } \quad r^{\prime}=90^{\circ}-r \\ & \sin r^{\prime}=\sin \left(90^{\circ}-r^{\prime}\right) \\ & =\cos \mathrm{r} \\ & \text { or } \quad \sin \mathrm{r}^{\prime}=\cos \mathrm{i} \\ & \therefore \frac{1}{\mu}=\frac{\sin \mathrm{i}}{\cos \mathrm{i}} \text { or } \frac{1}{\mu}=\tan \mathrm{i} \\ & \text { or } \quad \sin \mathrm{i}_{\mathrm{C}}=\tan \mathrm{i}=\tan \mathrm{r} \\ & \end{aligned}
The critical angle for pair of media is, \mathrm{i_{C}=tan\ i=tan\ r}

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Divya Prakash Singh

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