Question

In YDSE apparatus as shown in figure wavelength of light used in $\lambda .$ The screen is moved away from the source with a constant speed $V$. Initial distance between screen and plane of slits was $D$ . Suppose $P$ is the point where $5^{t h}$ order maxima was lying at $t=0,$ then after how much time third-order maxima will lie at this point $P$ on that screen?

• A. $\frac{2 D}{V}$
• B. $\frac{2 D}{3 V}$
• C. $\frac{3 D}{2 V}$
• D. $\frac{3 D}{V}$

Answer 1

Answer: (B)

At $t=0, \, \Delta x=5\lambda =\frac{y d}{D}$ .....(i)
After t times $\Delta x_{1}=3\lambda =\frac{y d}{D + v t}$ ......(ii)
Dividing (i) and (ii) we get
$\frac{5}{3}=\frac{D + v t}{D}$
$5D=3D+3vt$
$2D=3vt \, \, \Rightarrow \, \, t=\frac{2 D}{3 v}$