Two coherent sources S_1 and S_2 are separate | vedclass

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

Question

(B) Let the distance between the sources be $d = 4\lambda$. The detector is at a point $D$ on the $x$-axis at a distance $x$ from the origin (which is

Vedclass · Accepted Answer

$3$

Vedclass · Answer

(B) Let the distance between the sources be $d = 4\lambda$. The detector is at a point $D$ on the $x$-axis at a distance $x$ from the origin (which is $S_2$).The path difference $\Delta x$ between the waves reaching $D$ from $S_1$ and $S_2$ is given by $\Delta x = S_1D - S_2D$.In the right-angled triangle $\Delta S_1S_2D$,$S_1D = \sqrt{d^2 + x^2} = \sqrt{(4\lambda)^2 + x^2}$ and $S_2D = x$.For maxima,the path difference must be an integer multiple of the wavelength: $\Delta x = n\lambda$,where $n$ is an integer.So,$\sqrt{16\lambda^2 + x^2} - x = n\lambda$.Rearranging gives $\sqrt{16\lambda^2 + x^2} = n\lambda + x$.Squaring both sides: $16\lambda^2 + x^2 = n^2\lambda^2 + 2nx\lambda + x^2$.$16\lambda^2 - n^2\lambda^2 = 2nx\lambda$.$x = \frac{(16 - n^2)\lambda}{2n}$.For $x > 0$,we must have $16 - n^2 > 0$,which means $n^2 If $n=1$,$x = \frac{15\lambda}{2} = 7.5\lambda$.If $n=2$,$x = \frac{12\lambda}{4} = 3\lambda$.If $n=3$,$x = \frac{7\lambda}{6} \approx 1.17\lambda$.Thus,there are $3$ points where maxima are observed.

Two coherent sources $S_1$ and $S_2$ are separated by a distance four times the wavelength $\lambda$ of the source. The sources lie along the $y$-axis,whereas a detector moves along the $+x$-axis. Leaving the origin and far-off points,the number of points where maxima are observed is

Similar Questions

Two monochromatic beams of intensities $I$ and $4I$ respectively are superposed to form a steady interference pattern. The maximum and minimum intensities in the pattern are

If the wavelength of light is $4000 \text{ Å}$, then the number of waves in $1 \text{ mm}$ length will be . . . . . . -

The frequency of a light wave with a wavelength of $500 \, \mathring A$ is $....... \, Hz$.

When a light wave enters from air into water, which quantity does not change?

The contrast in the fringes in an interference pattern depends on

Vedclass Test Series

Exam Paper Generator

Online Exam Module