The wavelengths of light in two adjacent media are 3500 Å and 7000 Å, respectively. Then the critical angle for total internal reflection from their interface will be:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 30°
When light passes from one medium to another its frequency does not change, so its speed is proportional to its wavelength, and the refractive index is inversely proportional to the wavelength:
\( v = \nu\lambda \)
\( n \propto 1/v \propto 1/\lambda \)
The medium with the shorter wavelength (3500 Å) is the optically denser medium. Total internal reflection occurs for light going from it to the rarer medium, with
\( \displaystyle \sin C = \frac{n_{\mathrm{rarer}}}{n_{\mathrm{denser}}} = \frac{\lambda_{\mathrm{denser}}}{\lambda_{\mathrm{rarer}}} \)
\( \displaystyle \sin C = \frac{3500}{7000} = \frac{1}{2} \)
\( C = 30^\circ \)