The speed of light in two media c_1 and c_2 a | vedclass

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(D) The refractive index of a medium is defined as $\mu = \frac{c}{v}$,where $c$ is the speed of light in vacuum and $v$ is the speed of light in the

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$\sin^{-1}\left(\frac{3}{4}\right)$

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(D) The refractive index of a medium is defined as $\mu = \frac{c}{v}$,where $c$ is the speed of light in vacuum and $v$ is the speed of light in the medium.Given $c_1 = 1.5 	imes 10^8 \ m/s$ and $c_2 = 2 	imes 10^8 \ m/s$.Since $c_1  \mu_2$. Thus,medium $1$ is the denser medium and medium $2$ is the rarer medium.The condition for total internal reflection occurs when light travels from a denser medium to a rarer medium.The critical angle $	heta_C$ is given by the formula $\sin 	heta_C = \frac{\mu_2}{\mu_1}$.Since $\mu = \frac{c}{v}$,we have $\frac{\mu_2}{\mu_1} = \frac{c/c_2}{c/c_1} = \frac{c_1}{c_2}$.Substituting the given values,$\sin 	heta_C = \frac{1.5 	imes 10^8}{2 	imes 10^8} = \frac{1.5}{2} = \frac{3}{4}$.Therefore,$	heta_C = \sin^{-1}\left(\frac{3}{4}ight)$.

The speed of light in two media $c_1$ and $c_2$ are $1.5 \times 10^8 \ m/s$ and $2 \times 10^8 \ m/s$ respectively. If the light undergoes total internal reflection,the critical angle between the two media is

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