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Physics · 2025 · 5 marks
CBSE 2025 · Region 2 · Set 1 · Q33
(a) (i) A thin pencil of length ( f / 4 ) is placed coinciding with the principal axis of a mirror of focal length f. The image of the pencil is real…
(i)
A thin pencil of length ( $\displaystyle \mathrm{f} / 4$ ) is placed coinciding with the principal axis of a mirror of focal length f. The image of the pencil is real and enlarged, just touches the pencil. Calculate the magnification produced by the mirror.
(ii)
A ray of light is incident on a refracting face AB of a prism ABC at an angle of $\displaystyle 45^{\circ}$. The ray emerges from face AC and the angle of deviation is $\displaystyle 15^{\circ}$. The angle of prism is $\displaystyle 30^{\circ}$. Show that the emergent ray is normal to the face AC from which it emerges out. Find the refraction index of the material of the prism.
(i)
Light consisting of two wavelengths $\displaystyle 600$ nm and $\displaystyle 480$ nm is used to obtain interference fringes in a double slit experiment. The screen is placed $\displaystyle 1.0$ m away from slits which are $\displaystyle 1.0$ nm apart.
(1)
Calculate the distance of the third bright fringe on the screen from the central maximum for wavelength $\displaystyle 600$ nm.
(2)
Find the least distance from the central maximum where the bright fringes due to both the wavelengths coincide.
(ii)(1)
Draw the variation of intensity with angle of diffraction in single slit diffraction pattern. Write the expression for value of angle corresponding to zero intensity locations.
(2)
In what way diffraction of light waves differs from diffraction of sound waves?
Marking-scheme solution
(a)(i)
As the pencil lies between f and 2f such that one end of the pencil coincides with 2f.
Position of the other end $\displaystyle (u)=-\left(2 f-\frac{f}{4}\right)=-\frac{7 f}{4}$
Magnification $\displaystyle (m)=\frac{f}{f-u}$
$\displaystyle =\frac{-f}{-f-\left(-\dfrac{7 f}{4}\right)}$
$\displaystyle m=-\frac{4}{3}$
As the pencil lies between f and 2f such that one end of the pencil coincides with 2f.
Position of the other end $\displaystyle (u)=-\left(2 f-\frac{f}{4}\right)=-\frac{7 f}{4}$
$\displaystyle \frac{1}{v}+\frac{1}{u}=\frac{1}{f}$
$\displaystyle \frac{1}{v}-\frac{4}{7 f}=-\frac{1}{f}$
$\displaystyle \frac{1}{v}=-\frac{1}{f}+\frac{4}{7 f}$
$\displaystyle v=-\frac{7 f}{3}$
$\displaystyle m=-\frac{v}{u}=-\frac{4}{3}$
For prism:
$\displaystyle i+e=A+\delta$
$\displaystyle 45^{\circ}+e=30^{\circ}+15^{\circ}$
$\displaystyle \therefore e=0^{\circ}$
Hence, $\displaystyle r_{2}=0^{\circ}$
$\displaystyle \therefore$ Emergent ray is perpendicular to face AC.
$\displaystyle r_{1}+r_{2}=A$
As $\displaystyle r_{2}=0$, hence $\displaystyle r_{1}=30^{\circ}$
Refractive index $\displaystyle (n)=\frac{\sin i}{\sin r}=\frac{\sin 45^{\circ}}{\sin 30^{\circ}}$
$\displaystyle n=\sqrt{2}$
(b)
(1)
Distance of the $\displaystyle n^{\text {th }}$ bright fringe from the central maximum $\displaystyle \left(x_{n}\right)=\frac{n \lambda D}{d}$
For $\displaystyle n=3$:
$\displaystyle x_{3}=\frac{3 \times 600 \times 10^{-9} \times 1}{1 \times 10^{-3}}$
$\displaystyle =1.8 \times 10^{-3} \mathrm{~m}=1.8 \mathrm{~mm}$
(2)
$\displaystyle n_{1} \lambda_{1}=n_{2} \lambda_{2}$
$\displaystyle n_{1} \times 600=n_{2} \times 480$
$\displaystyle \frac{n_{1}}{n_{2}}=\frac{480}{600}=\frac{4}{5}$
Position of the $\displaystyle 4^{\text {th }}$ bright fringe of $\displaystyle 600$ nm $\displaystyle =\frac{4 \times 600 \times 10^{-9} \times 1}{1 \times 10^{-3}}=2.4 \mathrm{~mm}$
Position of the $\displaystyle 5^{\text {th }}$ bright fringe of $\displaystyle 480$ nm $\displaystyle =\frac{5 \times 480 \times 10^{-9} \times 1}{1 \times 10^{-3}}=2.4 \mathrm{~mm}$
(ii)(1)
Angle of diffraction for zero intensity, $\displaystyle \theta=\frac{n \lambda}{a} ; n=1,2,3 \ldots$
(2)
Diffraction of the light waves is not generally seen as compared to diffraction of sound waves as light waves have low wavelength.
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