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)
B
cos1(μ2)
C
2cos1(μ)
D
2sin1(μ2)

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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