CBSE 2025 · Region 6 · Set 1 · Q18 · 2 marks
Find the intensity at a point on the screen in Young's double slit experiment, at which the interfering waves of intensity $\displaystyle \mathrm{I}_{0}$ each, have a path difference of (i) $\displaystyle \frac{\lambda}{3}$, and (ii) $\displaystyle \frac{\lambda}{2}$.A point source of light in air is kept at a distance of $\displaystyle 12$ cm in front of a convex spherical surface of glass of refractive index $\displaystyle 1.5$ and radius of curvature $\displaystyle 30$ cm. Find the nature and position of the image formed.
Find the intensity at a point on the screen in Young's double slit experiment, at which the interfering waves of intensity $\displaystyle \mathrm{I}_{0}$ each, have a path difference of (i) $\displaystyle \frac{\lambda}{3}$, and (ii) $\displaystyle \frac{\lambda}{2}$.
A point source of light in air is kept at a distance of $\displaystyle 12$ cm in front of a convex spherical surface of glass of refractive index $\displaystyle 1.5$ and radius of curvature $\displaystyle 30$ cm. Find the nature and position of the image formed.
Marking-scheme solution
(a) Finding the intensity for path difference of
(i) \[\begin{aligned}
\Delta \phi & =\frac{2 \pi}{\lambda} \cdot \Delta x \\
\Delta \phi & =\frac{2 \pi}{\lambda} \cdot \frac{\lambda}{3}=\frac{2 \pi}{3} \\
\mathrm{I} & =4 \mathrm{I}_{0} \cos ^{2} \frac{\phi}{2} \\
\mathrm{I} & =4 \mathrm{I}_{0} \cos ^{2} \frac{\pi}{3} \\
\mathrm{I} & =\mathrm{I}_{0}
\end{aligned}
\]
(ii) \(\displaystyle \Delta \phi=\frac{2 \pi}{\lambda} \cdot \frac{\lambda}{2}=\pi\)
\[\begin{aligned}
& \mathrm{I}=4 \mathrm{I}_{0} \cos ^{2} \frac{\pi}{2} \\
& \mathrm{I}=0
\end{aligned}
\]
OR
(b) \[\begin{aligned}
& \frac{\mathrm{n}_{2}}{\mathrm{v}}-\frac{\mathrm{n}_{1}}{\mathrm{u}}=\frac{\mathrm{n}_{2}-\mathrm{n}_{1}}{\mathrm{R}} \\
& \frac{1.5}{\mathrm{v}}-\frac{1}{(-12)}=\frac{1.5-1}{30} \\
& \mathrm{v}=-22.5 \mathrm{~cm}
\end{aligned}
\]
Image is virtual and erect.
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CBSE Class 12 Physics past-paper question from the 2025board exam, with the answer as CBSE’s own marking scheme gives it. Where our answers come from.