Question:
The maximum number of possible interference maxima for slit separation equal to twice the wavelength in Young's double-slit experiment, is
The maximum number of possible interference maxima for slit separation equal to twice the wavelength in Young's double-slit experiment, is
Updated On: Jun 7, 2022
- infinite
- five
- three
- zero
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The Correct Option is B
Solution and Explanation
For possible interference maxima on the screen, the condition is
$d \sin \theta=n \lambda$ ...(i)
Given : $d=$ slit - width $=2 \lambda$
$\therefore 2 \lambda \sin \theta =n \lambda$
$\Rightarrow 2 \sin \theta =n$
The maximum value of $\sin \theta$ is 1 , hence, $n=2 \times 1=2$
Thus, E (i) must be satisfied by 5 integer values ie, $-2,-1,0,1,2$. Hence, the maximum number of possible interference maxima is $5 .$
$d \sin \theta=n \lambda$ ...(i)
Given : $d=$ slit - width $=2 \lambda$
$\therefore 2 \lambda \sin \theta =n \lambda$
$\Rightarrow 2 \sin \theta =n$
The maximum value of $\sin \theta$ is 1 , hence, $n=2 \times 1=2$
Thus, E (i) must be satisfied by 5 integer values ie, $-2,-1,0,1,2$. Hence, the maximum number of possible interference maxima is $5 .$
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Concepts Used:
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- Considering two waves interfering at point P, having different distances. Consider a monochromatic light source ‘S’ kept at a relevant distance from two slits namely S1 and S2. S is at equal distance from S1 and S2. SO, we can assume that S1 and S2 are two coherent sources derived from S.
- The light passes through these slits and falls on the screen that is kept at the distance D from both the slits S1 and S2. It is considered that d is the separation between both the slits. The S1 is opened, S2 is closed and the screen opposite to the S1 is closed, but the screen opposite to S2 is illuminating.
- Thus, an interference pattern takes place when both the slits S1 and S2 are open. When the slit separation ‘d ‘and the screen distance D are kept unchanged, to reach point P the light waves from slits S1 and S2 must travel at different distances. It implies that there is a path difference in the Young double-slit experiment between the two slits S1 and S2.
Read More: Young’s Double Slit Experiment