(A) The speed of light in air is $V_1 = \frac{x}{t_1}$.The speed of light in the denser medium is $V_2 = \frac{10x}{t_2}$.The refractive index of the

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$\sin^{-1}\left(\frac{10 t_1}{t_2}\right)$

(A) The speed of light in air is $V_1 = \frac{x}{t_1}$.The speed of light in the denser medium is $V_2 = \frac{10x}{t_2}$.The refractive index of the medium with respect to air is given by $n = \frac{V_1}{V_2} = \frac{x/t_1}{10x/t_2} = \frac{t_2}{10 t_1}$.The critical angle $\theta_c$ is defined by the relation $\sin \theta_c = \frac{1}{n}$.Substituting the value of $n$,we get $\sin \theta_c = \frac{1}{t_2 / (10 t_1)} = \frac{10 t_1}{t_2}$.Therefore,the critical angle is $\theta_c = \sin^{-1}\left(\frac{10 t_1}{t_2}\right)$.

Class 12 Physics Ray Optics and Optical Instruments Critical Angle and Total Internal Reflection

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Light travels a distance $x$ in time $t_1$ in air and $10x$ in time $t_2$ in another denser medium. What is the critical angle for this medium?

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A
$\sin^{-1}\left(\frac{10 t_1}{t_2}\right)$
B
$\sin^{-1}\left(\frac{t_2}{t_1}\right)$
C
$\sin^{-1}\left(\frac{10 t_2}{t_1}\right)$
D
$\sin^{-1}\left(\frac{t_1}{10 t_2}\right)$

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