The wavelengths of light in two liquids 'x' a | vedclass

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Question

(C) The refractive index $\mu$ is inversely proportional to the wavelength $\lambda$ $(\mu \propto 1/\lambda)$.Given: $\lambda_x = 3500 \ \mathring A$

Vedclass · Accepted Answer

$30$

Vedclass · Answer

(C) The refractive index $\mu$ is inversely proportional to the wavelength $\lambda$ $(\mu \propto 1/\lambda)$.Given: $\lambda_x = 3500 \ \mathring A$ and $\lambda_y = 7000 \ \mathring A$.The ratio of refractive indices is $\frac{\mu_y}{\mu_x} = \frac{\lambda_x}{\lambda_y} = \frac{3500}{7000} = \frac{1}{2}$.The critical angle $	heta_c$ for light traveling from a denser medium $(x)$ to a rarer medium $(y)$ is given by $\sin 	heta_c = \frac{\mu_y}{\mu_x}$.Substituting the values: $\sin 	heta_c = \frac{1}{2}$.Therefore,$	heta_c = \sin^{-1}(1/2) = 30^o$.

The wavelengths of light in two liquids '$x$' and '$y$' are $3500 \ \mathring A$ and $7000 \ \mathring A$ respectively. The critical angle of '$x$' with respect to '$y$' will be ...... $^o$.

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