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Question

When a ray of light enters a medium of refractive index $$\mu $$ from air. It is observed that the angle of refraction is half the angle of incidence. The angle of incidence is :


A
2cos1(μ2)
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B
cos1(μ2)
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C
2cos1(μ)
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D
2sin1(μ2)
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Solution

The correct option is A $$2 cos^{-1}(\frac{\mu }{2})$$
$${\text{r  =  }}\frac{{\text{i}}}{2}$$
Using Snell’s law,
$$\mu  = \frac{{{\text{sin i}}}}{{{\text{sin r}}}}$$
Substituting the values,
$$\mu  = \frac{{{\text{sin i}}}}{{{\text{sin }}\left( {\frac{{\text{i}}}{2}} \right)}}$$
$$\mu  = \frac{{{\text{2sin }}\left( {\frac{{\text{i}}}{2}} \right){\text{ cos }}\left( {\frac{{\text{i}}}{2}} \right)}}{{{\text{sin }}\left( {\frac{{\text{i}}}{2}} \right)}}$$
$$\frac{\mu }{2} = {\text{cos }}\left( {\frac{{\text{i}}}{2}} \right)$$
$$\frac{{\text{i}}}{2} = {\text{ co}}{{\text{s}}^{ - 1}}\left( {\frac{\mu }{2}} \right)$$
$${\text{i}} = {\text{ 2co}}{{\text{s}}^{ - 1}}\left( {\frac{\mu }{2}} \right)$$


Physics

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