CBSE 2022 · Region 3 · Set 3 · Q6 · 3 marks
A beam of light consisting of two wavelengths $\displaystyle 600$ nm and $\displaystyle 500$ nm is used in a Young's double slit experiment. The slit separation is $\displaystyle 1.0$ mm and the screen is kept $\displaystyle 0.60$ m away from the plane of the slits. Calculate :(i)the distance of the second bright fringe from the central maximum for wavelength $\displaystyle 500$ nm , and(ii)the least distance from the central maximum where the bright fringes due to both the wavelengths coincide.
A beam of light consisting of two wavelengths $\displaystyle 600$ nm and $\displaystyle 500$ nm is used in a Young's double slit experiment. The slit separation is $\displaystyle 1.0$ mm and the screen is kept $\displaystyle 0.60$ m away from the plane of the slits. Calculate :
(i)
the distance of the second bright fringe from the central maximum for wavelength $\displaystyle 500$ nm , and
(ii)
the least distance from the central maximum where the bright fringes due to both the wavelengths coincide.
Marking-scheme solution
(ii)
$\displaystyle \boldsymbol{n}_{1} \lambda_{1}=\boldsymbol{n}_{2} \lambda_{2}$
$\displaystyle \frac{\mathbf{1}}{\mathbf{2}}$
$$\begin{aligned}
\mathrm{n} \times $\displaystyle 600$ & =(\mathrm{n}+$\displaystyle 1$) $\displaystyle 500$
\mathrm{n} & =$\displaystyle 5$
x_{$\displaystyle 5$} & =\frac{5 \lambda D}{d}
x_{$\displaystyle 5$} & =\frac{$\displaystyle 2$ \times $\displaystyle 600$ \times $\displaystyle 10$^{-$\displaystyle 9$} \times $\displaystyle 0.60$}{$\displaystyle 10$^{-$\displaystyle 3$}}
& =$\displaystyle 1.8$ \mathrm{~mm}
\end{aligned}
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CBSE Class 12 Physics past-paper question from the 2022board exam, with the answer as CBSE’s own marking scheme gives it. Where our answers come from.