Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R).
Assertion (A): A ray of light travelling in water (refractive index 4/3) that meets the water-air surface at an angle of incidence of \( 45^\circ \) is totally reflected back into the water.
Reason (R): For total internal reflection, light must travel from an optically denser medium to an optically rarer medium.
In the light of the above statements, choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → (A) is false but (R) is true.
Assertion (A) A ray of light travelling in water (refractive index 4/3) that meets the water-air surface at an angle of incidence of \( 45^\circ \) is totally reflected back into the water. — False. The critical angle for the water-air surface is given by:
\( \begin{aligned} \sin i_c &= \frac{1}{n} \\ &= \frac{3}{4} \end{aligned} \)
\( \Rightarrow\; i_c\approx48.6^\circ \)
The angle of incidence, \( 45^\circ \), is less than \( i_c \), so the ray is partly reflected and partly refracted into the air. It is not totally reflected.
Reason (R) For total internal reflection, light must travel from an optically denser medium to an optically rarer medium. — True. When light goes into a rarer medium, the refracted ray bends away from the normal. The angle of refraction reaches \( 90^\circ \) at the critical angle. Beyond that angle, no refraction is possible and all the light is reflected.
NCERT (2026-27):
Summary – “2. The critical angle of incidence ic for a ray incident from a denser to rarer medium, is that angle for which the angle of refraction is 90°. For i > ic, total internal reflection occurs. …”
Total Internal Reflection – “The refractive index of denser medium 1 with respect to rarer medium 2 will be n12 = 1/sin ic. Some typical critical angles are listed in Table 9.1.”
