Two coherent narrow slits emitting light of w | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(D) The path difference between the two waves at point $P$ is given by $\Delta x = S_1P - S_2P$.For constructive interference (maxima),the path differ

Vedclass · Accepted Answer

$\frac{\sqrt{5}D}{2}$

Vedclass · Answer

(D) The path difference between the two waves at point $P$ is given by $\Delta x = S_1P - S_2P$.For constructive interference (maxima),the path difference must be an integer multiple of $\lambda$,i.e.,$\Delta x = n\lambda$.Given the geometry,the path difference is $\Delta x = S_1S_2 \cos 	heta$,where $S_1S_2 = 3\lambda$.Thus,$3\lambda \cos 	heta = n\lambda$,which implies $\cos 	heta = \frac{n}{3}$.For the smallest distance $x$ (excluding the central maximum at $x=0$),we look for the largest possible value of $n$ such that $n Then $\cos 	heta = \frac{2}{3}$.From the geometry,$\cos 	heta = \frac{D}{\sqrt{x^2 + D^2}}$.Equating the two expressions: $\frac{D}{\sqrt{x^2 + D^2}} = \frac{2}{3}$.Squaring both sides: $\frac{D^2}{x^2 + D^2} = \frac{4}{9}$.$9D^2 = 4x^2 + 4D^2$.$5D^2 = 4x^2$.$x^2 = \frac{5D^2}{4}$.$x = \frac{\sqrt{5}D}{2}$.

Similar Questions

When compound $X$ is oxidised by acidified potassium dichromate,compound $Y$ is formed. Compound $Y$ on reduction with $LiAlH_4$ gives $X$. $X$ and $Y$ respectively are :

If $(1, a)$ and $(b, 2)$ are conjugate points with respect to the circle $x^2+y^2=25$,then $4a+2b$ is equal to

If $\operatorname{adj}\begin{bmatrix} 1 & 0 & 2 \\ -1 & 1 & -2 \\ 0 & 2 & 1 \end{bmatrix} = \begin{bmatrix} 5 & a & -2 \\ 1 & 1 & 0 \\ -2 & -2 & b \end{bmatrix}$,then $\begin{bmatrix} a & b \end{bmatrix}$ is equal to

Velocity of sound waves in air is $330 \ m/s$. For a particular sound wave in air,a path difference of $40 \ cm$ is equivalent to a phase difference of $1.6 \pi$. The frequency of this wave is: (in $Hz$)

$A$ value of $n$ such that $\left(\frac{\sqrt{3}}{2}+\frac{i}{2}\right)^n=1$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module