Case: Read the passage and answer the question.
Young’s double-slit experiment (YDSE) shows the interference of light. Interference of light is the phenomenon in which light waves from two coherent sources overlap and combine in the same region of space. 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 two slits are illuminated in phase by the same source, so the central fringe is bright.
The waves from S1 and S2 reach the screen with intensities \( I \) and \( 4I \). The intensity on the screen, averaged over a region that contains many fringes, is
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → \( 5I \)
In interference the light energy is redistributed over the screen. The dark fringes lose what the bright fringes gain, and the total stays the same. At a point where the phase difference is \( \phi \), the intensity is the sum of the two intensities plus an interference term:
\( I_{\mathrm{R}}=I_1+I_2+2\sqrt{I_1I_2}\cos\phi \)
Across many fringes \( \cos\phi \) takes positive and negative values equally. So the interference term averages to zero. The average intensity is:
\( \begin{aligned} \bar{I} &= I_1+I_2 \\ &= I+4I \\ &= 5I \end{aligned} \)
The pattern itself varies between \( (\sqrt{4I}+\sqrt{I})^{2}=9I \) at the bright fringes and \( (\sqrt{4I}-\sqrt{I})^{2}=I \) at the dark fringes. The value \( 5I \) lies midway between them.
NCERT (2026-27):
Seeing the Single Slit Diffraction Pattern – “In interference and diffraction, light energy is redistributed. If it reduces in one region, producing a dark fringe, it increases in another region, producing a bright fringe. There is no gain or loss of energy, which is consistent with the principle of conservation of energy.”
Summary – “3. … When we consider the intensity of light due to these sources at the given point, there is an interference term in addition to the sum of the individual intensities. …”