Question:
Two beams of light having intensities I and 4I interfere to
produce a fringe pattern on a screen. The phase difference
between the beams is $\pi/2$ at point A and $\pi$ at point B. Then
the difference between resultant intensities at A and B is
Two beams of light having intensities I and 4I interfere to
produce a fringe pattern on a screen. The phase difference
between the beams is $\pi/2$ at point A and $\pi$ at point B. Then
the difference between resultant intensities at A and B is
Updated On: Jan 18, 2023
- 2 I
- 4 I
- 5 I
- 7 I
Show Solution
Verified By Collegedunia
The Correct Option is B
Solution and Explanation
$I(\phi)=I_1+I_2+2 \sqrt{I_1 I_2} cos \, \phi \hspace20mm ...(i)$
Here,$ \, \, \, \, \, I_1=I \, and \, I_2=4I$
At point A, $\phi=\frac{\pi}{2}$
$\therefore \, \, \, \, \, \, \, \, I_A=I+4I=5I$
At point B, $\phi=\pi$
$\therefore \, \, \, \, \, \, \, \, \, I_B=I+4I-4I=I$
$\therefore \, \, \, I_A-I_B=4I$
NOTE E (i) for resultant intensity can be applied only when the
sources are coherent. In the question it is given that the rays
interfere. Interference takes place only when the sources are
coherent. That is why we applied equation number (i). When the
sources are incoherent, the resultant intensity is given by I = $I_1+I_2$
Here,$ \, \, \, \, \, I_1=I \, and \, I_2=4I$
At point A, $\phi=\frac{\pi}{2}$
$\therefore \, \, \, \, \, \, \, \, I_A=I+4I=5I$
At point B, $\phi=\pi$
$\therefore \, \, \, \, \, \, \, \, \, I_B=I+4I-4I=I$
$\therefore \, \, \, I_A-I_B=4I$
NOTE E (i) for resultant intensity can be applied only when the
sources are coherent. In the question it is given that the rays
interfere. Interference takes place only when the sources are
coherent. That is why we applied equation number (i). When the
sources are incoherent, the resultant intensity is given by I = $I_1+I_2$
Was this answer helpful?
0
0
Top JEE Advanced Physics Questions
- Yellow light is used in a single slit diffraction experiment with slit width of 0.6 mm. If yellow light is replaced by X-rays, then the observed pattern will reveal
- The size of the image of an object, which is at infinity, as formed by a convex lens of focal length 30 cm is 2 cm. If a concave lens of focal length 20 cm is placed between the convex lens and the image at a distance of 26 cm from the convex lens, calculate the new size of the image.
- A concave lens of glass, refractive index 1.5 has both surfaces of same radius of curvature R. On immersion in a medium of refractive index 1.75, it will behave as a
- The position vector $\vec{r}$ of a particle of mass $m$ is given by the following equation $\vec{r}(t)=\alpha t^{3} \hat{i}+\beta t^{2} \hat{j}$ where $\alpha=\frac{10}{3} \,ms ^{-3}, \beta=5\, ms ^{-2}$ and $m =0.1 \,kg$. At $t =1\, s$, which of the following statement (s) is (are) true about the particle?
- In an n-p-n transistor circuit, the collector current is 10 mA. If 90% of the electrons emitted reach the collector
View More Questions
Top JEE Advanced single slit diffraction Questions
Top JEE Advanced Questions
- Yellow light is used in a single slit diffraction experiment with slit width of 0.6 mm. If yellow light is replaced by X-rays, then the observed pattern will reveal
- The size of the image of an object, which is at infinity, as formed by a convex lens of focal length 30 cm is 2 cm. If a concave lens of focal length 20 cm is placed between the convex lens and the image at a distance of 26 cm from the convex lens, calculate the new size of the image.
- A concave lens of glass, refractive index 1.5 has both surfaces of same radius of curvature R. On immersion in a medium of refractive index 1.75, it will behave as a
- The position vector $\vec{r}$ of a particle of mass $m$ is given by the following equation $\vec{r}(t)=\alpha t^{3} \hat{i}+\beta t^{2} \hat{j}$ where $\alpha=\frac{10}{3} \,ms ^{-3}, \beta=5\, ms ^{-2}$ and $m =0.1 \,kg$. At $t =1\, s$, which of the following statement (s) is (are) true about the particle?
- In an n-p-n transistor circuit, the collector current is 10 mA. If 90% of the electrons emitted reach the collector
View More Questions
Concepts Used:
Single Slit Diffraction
In the single-slit diffraction experiment, we can examine the bending phenomenon of light or diffraction that causes light from a coherent source to hinder itself and produce an extraordinary pattern on the screen called the diffraction pattern.
Read More: Difference Between Diffraction and Interference
Central Maximum
