The critical angle of a transparent medium with respect to air is \(45^\circ\). A ray inside the medium meets the medium–air surface at an angle of incidence of \(30^\circ\). The angle of refraction in air is
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → \(45^\circ\)
The angle of incidence is less than the critical angle, so the ray is refracted into air. The critical angle gives \( n_{21} \) for the pair, and Snell’s law then gives the angle of refraction.
\( \begin{aligned} n_{21} &= \sin 45^\circ \\ &= \frac{1}{\sqrt{2}} \end{aligned} \)
\( \begin{aligned} \sin r &= \frac{\sin i}{n_{21}} \\ &= \frac{1/2}{1/\sqrt{2}} \\ &= \frac{1}{\sqrt{2}} \end{aligned} \)
\( r=45^\circ \)
The ray bends away from the normal, from \(30^\circ\) to \(45^\circ\). Hence, the angle of refraction in air is \(45^\circ\).
NCERT (2026-27):
Total Internal Reflection – “… there is an upper limit to the value of sin i for which the law can be satisfied, that is, i = ic such that”
\( \displaystyle \sin i_c=n_{21} \)\( \qquad (9.12) \)
Refraction – “(ii) The ratio of the sine of the angle of incidence to the sine of angle of refraction is constant. … We have”
\( \displaystyle \frac{\sin i}{\sin r}=n_{21} \)\( \qquad (9.10) \)
“where n21 is a constant, called the refractive index of the second medium with respect to the first medium. …”