In the Young's double slit experiment using a | vedclass

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

Question

(B) The intensity at any point in the interference pattern is given by $I = I_{max} \cos^2(\frac{\phi}{2})$,where $\phi$ is the phase difference.Given

Vedclass · Accepted Answer

$(2n+1) \frac{\lambda}{4}$

Vedclass · Answer

(B) The intensity at any point in the interference pattern is given by $I = I_{max} \cos^2(\frac{\phi}{2})$,where $\phi$ is the phase difference.Given that the intensity is half of the peak intensity,$I = \frac{I_{max}}{2}$.Substituting this into the equation: $\frac{I_{max}}{2} = I_{max} \cos^2(\frac{\phi}{2})$.This simplifies to $\cos^2(\frac{\phi}{2}) = \frac{1}{2}$,which means $\cos(\frac{\phi}{2}) = \pm \frac{1}{\sqrt{2}}$.Thus,$\frac{\phi}{2} = \frac{\pi}{4}, \frac{3\pi}{4}, \frac{5\pi}{4}, \dots$,which implies $\phi = \frac{\pi}{2}, \frac{3\pi}{2}, \frac{5\pi}{2}, \dots$.In general,$\phi = (2n+1) \frac{\pi}{2}$.Since the path difference $\Delta x = \frac{\lambda}{2\pi} \phi$,we substitute $\phi$:$\Delta x = \frac{\lambda}{2\pi} 	imes (2n+1) \frac{\pi}{2} = (2n+1) \frac{\lambda}{4}$.

In the Young's double slit experiment using a monochromatic light of wavelength $\lambda$,the path difference (in terms of an integer $n$) corresponding to any point having half the peak intensity is:

Similar Questions

If the intensity of each wave in the observed interference pattern in Young's double slit experiment is $I_0$,then for some point $P$ where the phase difference is $\phi$,the resultant intensity $I$ will be:

In $Y.D.S.E.$ using light of wavelength $\lambda$,the intensity of light at a point on the screen with path difference $\lambda$ is $M$ units. Calculate the intensity of light at a point where the path difference is $\frac{\lambda}{3}$.

Two coherent sources of intensity ratio $\alpha$ interfere. The value of $\frac{I_{max} - I_{min}}{I_{max} + I_{min}}$ is

The intensity ratio of the two interfering beams of light is $\beta$. What is the value of $\frac{I_{\max} - I_{\min}}{I_{\max} + I_{\min}}$?

Vedclass Test Series

Exam Paper Generator

Online Exam Module