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Physics Question on Ray optics and optical instruments

A ray of light is incident on the surface of separation of a medium with the velocity oflight at an angle 45∘45^{\circ} and is refracted in the medium at an angle 30∘30^{\circ}. What will be the velocity of light in the medium?

A

1.96×108 ms−11.96 \times 10^8\, ms^{-1}

B

2.12×108 ms−12.12 \times 10^8\, ms^{-1}

C

3.18×108 ms−13.18 \times 10^8\, ms^{-1}

D

3.33×108 ms−13.33 \times 10^8\, ms^{-1}

Answer

2.12×108 ms−12.12 \times 10^8\, ms^{-1}

Explanation

Solution

c1c2=sin⁡isin⁡r\frac{c_{1}}{c_{2}}=\frac{\sin i}{\sin r}
∴3×108c2=sin⁡45∘sin⁡30∘=0.7070.5\therefore \frac{3 \times 10^{8}}{c_{2}}=\frac{\sin 45^{\circ}}{\sin 30^{\circ}}=\frac{0.707}{0.5}
So, c2=3×108×0.50.707c_{2}=\frac{3 \times 10^{8} \times 0.5}{0.707}
=2.12×108 ms−1=2.12 \times 10^{8}\, ms ^{-1}