Monochromatic light falls from air on the surface of water of refractive index 4/3. Part of the light is reflected, and part is refracted into the water. The ratio of the wavelength of the reflected light to that of the refracted light is
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → \(4:3\)
Reflection and refraction do not change the frequency of light. The reflected light goes back into air, so its speed and wavelength stay the same. The refracted light moves more slowly in water, so its wavelength becomes shorter. With the same frequency, wavelength is proportional to speed.
\( \begin{aligned} \frac{\lambda_{reflected}}{\lambda_{refracted}} &= \frac{\lambda_1}{\lambda_2} \\ &= \frac{v_1}{v_2} \\ &= \frac{n_2}{n_1} \\ &= \frac{4/3}{1} \\ &= \frac{4}{3} \end{aligned} \)
Hence, the wavelengths of the reflected and the refracted light are in the ratio \(4:3\).
NCERT (2026-27):
Example 10.1 – “(a) Reflection and refraction arise through interaction of incident light with the atomic constituents of matter. Atoms may be viewed as oscillators, which take up the frequency of the external agency (light) causing forced oscillations. The frequency of light emitted by a charged oscillator equals its frequency of oscillation. Thus, the frequency of scattered light equals the frequency of incident light.”
Refraction of a plane wave – “… Further, if λ1 and λ2 denote the wavelengths of light in medium 1 and medium 2, respectively and if the distance BC is equal to λ1 then the distance AE will be equal to λ2 … thus,”
\( \displaystyle \frac{\lambda_1}{\lambda_2}=\frac{BC}{AE}=\frac{v_1}{v_2}\quad \text{or}\quad \frac{v_1}{\lambda_1}=\frac{v_2}{\lambda_2} \)\( \qquad (10.7) \)
Refraction of a plane wave – “… Now, if c represents the speed of light in vacuum, then,”
\( \displaystyle n_1=\frac{c}{v_1} \)\( \qquad (10.4) \)
“and”
\( \displaystyle n_2=\frac{c}{v_2} \)\( \qquad (10.5) \)
“are known as the refractive indices of medium 1 and medium 2, respectively. …”