✓ Board-verified
Physics · 2024 · 5 marks
CBSE 2024 · Region 5 · Set 1 · Q33
(a) (i) A plane light wave propagating from a rarer into a denser medium, is incident at an angle i on the surface separating two media. Using…
(a)(i)
A plane light wave propagating from a rarer into a denser medium, is incident at an angle i on the surface separating two media. Using Huygen's principle, draw the refracted wave and hence verify Snell's law of refraction.
(ii)
In a Young's double slit experiment, the slits are separated by $\displaystyle 0.30$ mm and the screen is kept $\displaystyle 1.5$ m away. The wavelength of light used is $\displaystyle 600$ nm . Calculate the distance between the central bright fringe and the $\displaystyle 4^{\text {th }}$ dark fringe.
OR 33. (b) (i) Discuss briefly diffraction of light from a single slit and draw the shape of the diffraction pattern.
(ii)
An object is placed between the pole and the focus of a concave mirror. Using mirror formula, prove mathematically that it produces a virtual and an enlarged image.
Marking-scheme solution
(i)
Considering triangles ABC and AEC:
$\displaystyle \sin i=\frac{B C}{A C}=\frac{v_{1} \tau}{A C}$ ------($\displaystyle 1$)
$\displaystyle \sin r=\frac{A E}{A C}=\frac{v_{2} \tau}{A C}$ ------($\displaystyle 2$)
From equation ($\displaystyle 1$) and equation ($\displaystyle 2$):
$\displaystyle \frac{\sin i}{\sin r}=\frac{v_{1}}{v_{2}}$ ------($\displaystyle 3$)
If c represents the speed of light in vacuum, then:
$\displaystyle n_{1}=\frac{c}{v_{1}}$ and $\displaystyle n_{2}=\frac{c}{v_{2}}$
In terms of refractive indices:
$\displaystyle n_{1} \sin i=n_{2} \sin r$
which is Snell's law of refraction.
(ii)
$\displaystyle X_{4}=\frac{(2 n-1) \lambda D}{2 d}$
$\displaystyle X_{4}=\frac{(2 \times 4-1) \times 600 \times 10^{-9} \times 1.5}{2 \times 0.3 \times 10^{-3}}$
$\displaystyle =1.05 \times 10^{-2} \mathrm{~m}$
(i)
A beam of light falls normally on a single slit and bends around its corners. This phenomenon is called diffraction.
When a beam of light falls normally on a narrow single slit, the diffracted light goes on to meet on a screen. It is observed that at the centre of the screen the intensity is maximum and goes on decreasing as one moves away from the centre on either side of the screen.
(ii)
$\displaystyle \frac{1}{f}=\frac{1}{v}+\frac{1}{u}$
$\displaystyle v=\frac{u f}{u-f}$
Following the new Cartesian sign convention:
$\displaystyle v=\frac{(-u)(-f)}{-u-(-f)}$
$\displaystyle v=\frac{u f}{f-u}$ as $\displaystyle f>u$
v is +ve, so the image is virtual.
$\displaystyle m=-\frac{v}{u}=\frac{f}{f-u}>1$ i.e. enlarged image.
More from Wave Optics
- Define 'wavefront' of a light wave. A plane wavefront is refracted from a convex lens. Draw the shape of the refracted wavefront. A plane wave…2025
- A double slit set-up was initially placed in a tank filled with water and the interference pattern was obtained using a laser light. When water is…2025
- The phenomenon of interference is shown by2026
- Assertion: In interference and diffraction of light, light energy reduces in one region producing a dark fringe. It increases in another region and…2024
- Using the Huygens' principle, briefly describe reflection of a plane wavefront from a reflecting surface. Hence, prove the laws of reflection.2025
- Assertion: In a Young's double-slit experiment, interference pattern is not observed when two coherent sources are infinitely close to each other.…2024
- (i) Give any two differences between the interference pattern obtained in Young's double-slit experiment and a diffraction pattern due to a single…2024
- A plane wave-front propagating in a medium of refractive index ' μ_1 ' is incident on a plane surface making an angle of incidence (i). It enters…2023
CBSE Class 12 Physics past-paper question from the 2024 board exam, with the answer as CBSE’s own marking scheme gives it. Where our answers come from.