Question

In a YDSE experiment shown, monochromatic light of wavelength $\lambda$ is used. Given $D=2m$ and $\frac{d}{\lambda }=100$. The screen starts from rest and accelerates with $2m/s^2$ at $t=0$. If $C$ is the centre of the line joining $S_1{S}_2$ and meeting the screen, then (Assume $d>>\lambda$)

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

Answer 1

Answer: (A), (B), (C)

The correct options are
A Velocity of the third maxima at $t=3s$ is $6.002m/s$
B $C$ will always be the central maxima.
C Fringe Width increases with increase in time.

Let $D^{\prime }$ be distance between slits and screen after time interval $t$
$D^{\prime }=D+\frac{a{t}^2}{2}$
After time $t=3s$, velocity of central bright fridge $\left(V_c\right)=at=6m/s$
Vectorially $\left(\overrightarrow{V_c}\right)=6\hat{i}m/s$
a)For $3^{rd}$ maximum $\frac{yd}{D}=3\lambda$ $\Rightarrow y=\frac{3\lambda D^{\prime }}{d}$
Velocity of $3^{rd}$ maxima wrt $CBF$
$\overrightarrow{V_{3c}}=\frac{dy}{dt}\hat{j}=\frac{3\lambda }{d}\left[at\right]\hat{j}$
$\Rightarrow \overrightarrow{V_3}-\overrightarrow{V_c}=\frac{3}{100}\times 6\hat{j}=0.18\hat{j}m/s$
$\Rightarrow \overrightarrow{V_3}=0.18\hat{j}+6\hat{i}$
$\Rightarrow |\overrightarrow{V_3}|=6.002m/s$

$b)\beta =\frac{\lambda D^{\prime }}{d}=\frac{\lambda }{d}(D+\frac{1}{2}a{t}^2)$
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.