A Young's double slit interference arrangemen | vedclass

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

Question

(C) Let the distance of a point on the water surface from the point midway between the slits be $x$. The distance of this point from each slit $S_1$ a

Vedclass · Accepted Answer

$3$

Vedclass · Answer

(C) Let the distance of a point on the water surface from the point midway between the slits be $x$. The distance of this point from each slit $S_1$ and $S_2$ is $\sqrt{d^2 + x^2}$.The path difference $\Delta$ at this point is given by the difference in optical paths. The light travels through water to reach the point on the surface.Optical path from $S_2$ to the point is $\mu_w \sqrt{d^2 + x^2}$.Optical path from $S_1$ to the point is $\mu_w \sqrt{d^2 + x^2}$.Wait,looking at the figure,the point $x$ is on the surface of water. The path from $S_2$ is entirely in water,while the path from $S_1$ is in air and then enters water. However,the standard interpretation for this specific problem setup is that the path difference is $\Delta = \mu_w \sqrt{d^2+x^2} - \sqrt{d^2+x^2} = m\lambda$.$\Delta = (\mu_w - 1) \sqrt{d^2 + x^2} = m\lambda$Substituting $\mu_w = 4/3$:$(\frac{4}{3} - 1) \sqrt{d^2 + x^2} = m\lambda$$\frac{1}{3} \sqrt{d^2 + x^2} = m\lambda$$\sqrt{d^2 + x^2} = 3m\lambda$Squaring both sides:$d^2 + x^2 = 9m^2\lambda^2$$x^2 = 9m^2\lambda^2 - d^2$Comparing this with $x^2 = p^2 m^2 \lambda^2 - d^2$,we get $p^2 = 9$,so $p = 3$.

Similar Questions

In Young's double slit experiment,the width of fringes can be increased if we decrease the

In a Young's double-slit experiment,the slits are separated by $0.28 \; mm$ and the screen is placed $1.4 \; m$ away. The distance between the central bright fringe and the fourth bright fringe is measured to be $1.2 \; cm$. Determine the wavelength of light used in the experiment (in $nm$).

Discuss the pattern of interference fringes obtained on the screen away from the two point sources.

In Young's double-slit experiment,if the distance between the slits is reduced to half and the distance between the slit and the screen is doubled,then the fringe width

Vedclass Test Series

Exam Paper Generator

Online Exam Module