Case: Read the passage and answer the question.
YDSE is the abbreviation used for Young’s double-slit experiment, which shows the interference of light. Interference of light is the phenomenon in which two light waves meet each other while travelling in the same medium. A light source is kept behind a wall in which two slits, S1 and S2, are made. On the screen there appears a pattern of alternate bright and dark fringes. The central fringe is always bright.
Two slits are illuminated by light of wavelength 5890 Å and the angular fringe width (the angular separation between adjacent bright fringes) is \( 0.2^\circ \). If the whole apparatus is immersed in water (refractive index 4/3), the angular fringe width becomes
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → \( 0.15^\circ \)
The bright fringes lie at \( x_n=n\lambda D/d \), so neighbouring fringes are \( \beta=\lambda D/d \) apart. Seen from the slits, the angular fringe width is
\( \begin{aligned} \theta &= \frac{\beta}{D} \\ &= \frac{\lambda}{d} \end{aligned} \)
When light enters water its frequency stays the same. Its speed falls to \( c/n \), so the wavelength decreases to \( \lambda/n \). The slit separation does not change.
\( \begin{aligned} \theta' &= \frac{\lambda/n}{d} \\ &= \frac{\theta}{n} \end{aligned} \)
\( \begin{aligned} \theta' &= \frac{0.2^\circ}{4/3} \\ &= 0.2^\circ\times\frac{3}{4} \\ &= 0.15^\circ \end{aligned} \)
The ratio \( \theta'/\theta \) depends only on the refractive index, so the value 5890 Å of the wavelength is not needed.
NCERT (2026-27):
Refraction of a Plane Wave – “… The above equation implies that when a wave gets refracted into a denser medium (v1 > v2) the wavelength and the speed of propagation decrease but the frequency ν(= v/λ) remains the same.”