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Question

In a YDSE experiment shown, monochromatic light of wavelength λ is used. Given D=2 m and dλ=100. The screen starts from rest and accelerates with 2 m/s2 at t=0. If C is the centre of the line joining S1S2 and meeting the screen, then (Assume d>>λ)

A
Velocity of the third maxima at t=3 s is 6.002 m/s
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B
C will always be the central maxima.
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C
Fringe Width increases with increase in time.
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D
Velocity of third maxima is independent of time.
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Solution

The correct options are
A Velocity of the third maxima at t=3 s is 6.002 m/s
B C will always be the central maxima.
C Fringe Width increases with increase in time.
Let D be distance between slits and screen after time interval t
D=D+at22
After time t=3 s, velocity of central bright fridge (Vc)=at=6 m/s
Vectorially (Vc)=6 ^i m/s
a)For 3rd maximum ydD=3λ y=3λDd
Velocity of 3rd maxima wrt CBF
V3c=dydt^j=3λd[at]^j
V3Vc=3100×6^j=0.18^j m/s
V3=0.18^j+6^i
|V3|=6.002 m/s

b)β=λDd=λd(D+12at2)
Fringe width increases with increase in time.
c) C wil always be a maxima as the path difference does not change
d) Velocity of third maxima depends on time.

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