CBSE 2024 · Region 2 · Set 1 · Q18 · 2 marks
Two waves, each of amplitude 'a' and frequency ' $\displaystyle \omega$ ' emanating from two coherent sources of light superpose at a point. If the phase difference between the two waves is $\displaystyle \phi$, obtain an expression for the resultant intensity at that point.What is the effect on the interference pattern in Young's double-slit experiment when (i) the source slit is moved closer to the plane of the slits, and (ii) the separation between the two slits is increased? Justify your answers.
Two waves, each of amplitude 'a' and frequency ' $\displaystyle \omega$ ' emanating from two coherent sources of light superpose at a point. If the phase difference between the two waves is $\displaystyle \phi$, obtain an expression for the resultant intensity at that point.
What is the effect on the interference pattern in Young's double-slit experiment when (i) the source slit is moved closer to the plane of the slits, and (ii) the separation between the two slits is increased? Justify your answers.
Marking-scheme solution
$\displaystyle x_{1}=a \cos \omega t$
$\displaystyle x_{2}=a \cos (\omega t+\phi)$
$\displaystyle x=x_{1}+x_{2}$
$\displaystyle =a(\cos \omega t+\cos (\omega t+\phi))$
$\displaystyle =a\left(2 \cos \left(\omega t+\frac{\phi}{2}\right) \cos \frac{\phi}{2}\right)$
$\displaystyle =2 a \cos \frac{\phi}{2} \cos \left(\omega t+\frac{\phi}{2}\right)$
Intensity:
$\displaystyle I=K(\text { amplitude })^{2}$ where K is a constant.
$\displaystyle =K\left(2 a \cos \frac{\phi}{2}\right)^{2}$
$\displaystyle =4 I_{0} \cos ^{2} \frac{\phi}{2}$
$\displaystyle I_{0}=K a^{2}=$ intensity of each incident wave.
(b)
Sharpness of the interference pattern decreases.
$\displaystyle \frac{s}{S}<\frac{\lambda}{d}$
As S decreases, interference patterns produced by different parts of the source overlap and finally fringes disappear.
As the source slit is brought closer to the plane of the slits, the screen gets illuminated uniformly and fringes disappear.
(ii)
$\displaystyle \beta=\frac{\lambda D}{d}$
As d increases, $\displaystyle \beta$ decreases and fringes disappear.
Wave OpticsInterference of Light Waves and Young’s ExperimentApplyvery_short_answermedium
More from Wave Optics
- Assertion: In interference and diffraction of light, light energy reduces in one region producing a dark…2024 · asked 3×
- Assertion: In a Young's double-slit experiment, interference pattern is not observed when two coherent…2024 · asked 3×
- What are coherent sources? Why they are necessary for observing stable interference pattern? Draw a graph…2026 · asked 3×
- In a Young's double-slit experiment, the fringe width is found to be β. If the entire apparatus is immersed…2023 · asked 3×
- Assertion: In Young's double slit experiment all fringes are of equal width. Reason (R): The fringe width…2023 · asked 3×
- (i) A plane light wave propagating from a rarer into a denser medium, is incident at an angle i on the…2024 · asked 3×
- Assertion: Light added to light can produce darkness. Reason (R): When two coherent light waves interfere,…2026 · asked 3×
- In a Young's double-slit experiment, the screen is moved away from the plane of the slits. What will be its…2023 · asked 3×
CBSE Class 12 Physics past-paper question from the 2024board exam, with the answer as CBSE’s own marking scheme gives it. Where our answers come from.