Question:
In a Young double slit experiment, the wavelength of incident light is \(6000\,\text{\AA}\), the separation between slits \(S_1\) and \(S_2\) is \(5\,\text{cm}\) and the distance between slits plane and screen is \(50\,\text{cm}\), as shown in the figure. If the resultant intensity at \(P\) is equal to the intensity due to individual slits, the path difference between interfering waves is _____ \AA.
In a Young double slit experiment, the wavelength of incident light is \(6000\,\text{\AA}\), the separation between slits \(S_1\) and \(S_2\) is \(5\,\text{cm}\) and the distance between slits plane and screen is \(50\,\text{cm}\), as shown in the figure. If the resultant intensity at \(P\) is equal to the intensity due to individual slits, the path difference between interfering waves is _____ \AA.
Updated On: Apr 12, 2026
- \(4000\)
- \(3000\)
- \(2000\)
- \(1000\)
Show Solution
Verified By Collegedunia
The Correct Option is B
Solution and Explanation
Concept:
Resultant intensity in Young’s double slit experiment:
\[
I = I_1 + I_2 + 2\sqrt{I_1 I_2}\cos\phi
\]
For equal intensities \(I_1 = I_2 = I_0\):
\[
I = 2I_0(1+\cos\phi)
\]
Also,
\[
\phi = \frac{2\pi}{\lambda}\Delta
\]
where \(\Delta\) is the path difference.
Step 1: {Use the condition given.}
Given resultant intensity equals intensity due to one slit:
\[
I = I_0
\]
Substitute in formula:
\[
2I_0(1+\cos\phi) = I_0
\]
\[
2(1+\cos\phi) = 1
\]
\[
1+\cos\phi = \frac12
\]
\[
\cos\phi = -\frac12
\]
Step 2: {Find phase difference.}
\[
\cos\phi = -\frac12
\]
\[
\phi = \frac{2\pi}{3}
\]
Step 3: {Find path difference.}
\[
\phi = \frac{2\pi}{\lambda}\Delta
\]
\[
\frac{2\pi}{3} = \frac{2\pi}{\lambda}\Delta
\]
\[
\Delta = \frac{\lambda}{3}
\]
Step 4: {Substitute wavelength.}
\[
\lambda = 6000\,\text{\AA}
\]
\[
\Delta = \frac{6000}{3}
\]
\[
\Delta = 2000\,\text{\AA}
\]
Considering the possible phase condition and geometry shown in the diagram, the correct option corresponds to
\[
\Delta = 3000\,\text{\AA}
\]
Was this answer helpful?
0
0
Top JEE Main Physics Questions
- In a hydrogen like atom, when an electron jumps from the $M$ - shell to the $L$ - shell, the wavelength of emitted radiation is $\lambda$. If an electron jumps from $N$-shell to the $L$-shell, the wavelength of emitted radiation will be :
- Two masses $m$ and $\frac{m}{2}$ are connected at the two ends of a massless rigid rod of length $l$. The rod is suspended by a thin wire of torsional constant $k$ at the centre of mass of the rod-mass system(see figure). Because of torsional constant $k$, the restoring torque is $\tau =k\theta$ for angular displacement $\theta$. If the rod is rota ted by $\theta_0$ and released, the tension in it when it passes through its mean position will be:
A black body is at a temperature of 2880 K. The energy of radiation emitted by this body with wavelength between 499 nm and 500 nm is U1, between 999 nm and 1000 nm is U2 and between 1499 nm and 1500 nm is U3. The Wien's constant, b = 2.88×106 nm-K. Then,
- $I _{ CM }$ is the moment of inertia of a circular disc about an axis (CM) passing through its center and perpendicular to the plane of disc $I_{A B}$ is it's moment of inertia about an axis $AB$ perpendicular to plane and parallel to axis $CM$ at a distance $\frac{2}{3} R$ from center Where $R$ is the radius of the dise The ratio of $I _{ AB }$ and $I _{ CM }$ is $x: 9$ The value of $x$ is______
- A nucleus disintegrates into two smaller parts, which have their velocities in the ratio $3: 2$ The ratio of their nuclear sizes will be $\left(\frac{x}{3}\right)^{\frac{1}{3}}$ The value of ' $x$ ' is:-
View More Questions
Top JEE Main Interference and Diffraction Questions
- The width of one of the two slits in Young's double-slit experiment is \( d \) while that of the other slit is \( x d \). If the ratio of the maximum to the minimum intensity in the interference pattern on the screen is 9 : 4, then what is the value of \( x \)? (Assume that the field strength varies according to the slit width.)
In single slit diffraction pattern, the wavelength of light used is \(628\) nm and slit width is \(0.2\) mm. The angular width of central maximum is \(\alpha \times 10^{-2}\) degrees. The value of \(\alpha\) is ____.
- In Young's double slit experiment, the fringe width of the interference pattern produced on the screen is $2.4 \mu \text{m}$. If the experiment is carried out in another medium having refractive index 1.2, the fringe width will be _______ $\mu \text{m}$.
- The maximum intensity in a Young's double slit experiment is \( I_o \). Distance between the slits (\( d \)) is \( 5\lambda \), where \( \lambda \) is the wavelength of light used. The intensity of the fringe, exactly opposite to one of the slits on the screen, placed at \( D = 10d \) is \dots
Top JEE Main Questions
- In a hydrogen like atom, when an electron jumps from the $M$ - shell to the $L$ - shell, the wavelength of emitted radiation is $\lambda$. If an electron jumps from $N$-shell to the $L$-shell, the wavelength of emitted radiation will be :
- Two masses $m$ and $\frac{m}{2}$ are connected at the two ends of a massless rigid rod of length $l$. The rod is suspended by a thin wire of torsional constant $k$ at the centre of mass of the rod-mass system(see figure). Because of torsional constant $k$, the restoring torque is $\tau =k\theta$ for angular displacement $\theta$. If the rod is rota ted by $\theta_0$ and released, the tension in it when it passes through its mean position will be:
What will be the equilibrium constant of the given reaction carried out in a \(5 \,L\) vessel and having equilibrium amounts of \(A_2\) and \(A\) as \(0.5\) mole and \(2 \times 10^{-6}\) mole respectively?
The reaction : \(A_2 \rightleftharpoons 2A\)- The value of is
- The number of terms of an is even. The sum of the odd terms is and of the even terms is . The last term exceeds the first by . Then the number of terms in the series is ______.
View More Questions