In a young's double slit experiment, the fringe pattern is observ… - Vidyadip

MCQ

In a young's double slit experiment, the fringe pattern is observed on a screen placed at a distance $D$. The slits are separated by $d$ and are illuminated by light of wavelength $\lambda$. Find the distance from the central point where the intensity falls to half the maximum is

✓
$\frac{\lambda D}{4d}$
B
$\frac{\lambda D}{2d}$
C
$\frac{\lambda D}{d}$
D
$\frac{2}{3} \frac{\lambda D}{d}$

✓

Answer

Correct option: A.

$\frac{\lambda D}{4d}$

a
$I=I_{\max } \cos ^{2} \frac{\phi}{2}$

$\frac{I_{\max }}{2}=I_{\max } \cos ^{2} \frac{\phi}{2} \therefore \cos \frac{\phi}{2}=\frac{1}{\sqrt{2}}$

$\frac{\phi}{2}=\frac{\pi}{4} \quad \phi=\frac{\pi}{2}$

Path diff. $\Delta \mathrm{x}=\left(\frac{\lambda}{2 \pi}\right)(\Delta \phi)=\frac{\lambda}{2 \pi} \times \frac{\pi}{2} \Rightarrow \frac{\lambda}{4}$

Distance $\quad \mathrm{x}=\frac{\Delta \mathrm{D}}{\mathrm{d}}=\frac{\lambda}{4} \frac{\mathrm{D}}{\mathrm{d}}$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "M.C.Q (1 Marks)" from 10. Wave optics→10. Wave optics — all question types→Physics STD 12 Science question papers→CBSE Board STD 12 Science question papers→CBSE Board question paper generator→

Similar questions

The current flowing in a coil of resistance $90 \,\Omega$ is to be reduced by $90\%$. What value of resistance should be connected in parallel with it ............. $\Omega $

The current in a conductor is expressed as $I=3 t^2+4 t^3$, where $I$ is in Ampere and $t$ is in second. The amount of electric charge that flows through a section of the conductor during $t=1$ s to $t=2 \mathrm{~s}$ is_______ C.

Which of the following quantities do not change when a resistor connected to a battery is heated due to the current?

The energy of the em waves is of the order of $15\, keV.$ To which part of the spectrum does it belong?

An $LCR$ circuit contains $R = 50\, \Omega$ ,$L =\,1 \,mH $ and $C = \,0.1$ $\mu F$. The impedance of the circuit will be minimum for a frequency of

$A$ conductor is made of an isotropic material and has shape of a truncated cone. $A$ battery of constant emf is connected across it and its left end is earthed as shown in figure. If at a section distant $x$ from left end, electric field intensity, potential and the rate of generation of heat per unit length are $E, V$ and $H$ respectively, which of the following graphs is are correct?

A ray of light is incident on the surface of separation of a medium at an angle $45^o $ and is refracted in the medium at an angle $30^o .$ What will be the velocity of light in the medium

The distance of closest approach of an alpha particle is $d$ when it moves with a speed $V$ towards a nucleus.
Another alpha particle is projected with higher energy such that the new distance of the closest approach is $d/2.$ What is the speed of projection of the alpha particle in this case?

The mechanism of the hydrogen bomb is based on

Assertion : It is not possible to use ${}^{35}Cl$ as the fuel for fusion energy.

Reason : The binding energy of ${}^{35}Cl$ is too small.