Visible light of wavelength 6000 times 10^{-8 | vedclass

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

Question

(D) For a single slit diffraction,the condition for the $n^{th}$ minimum is given by $a \sin 	heta = n \lambda$,where $a$ is the slit width,$\lambda$

Vedclass · Accepted Answer

$25$

Vedclass · Answer

(D) For a single slit diffraction,the condition for the $n^{th}$ minimum is given by $a \sin 	heta = n \lambda$,where $a$ is the slit width,$\lambda$ is the wavelength,and $n = 1, 2, 3, ...$.For the second minimum $(n = 2)$,the angle is $	heta_2 = 60^{\circ}$.Thus,$a \sin 60^{\circ} = 2 \lambda$.$a \left( \frac{\sqrt{3}}{2} ight) = 2 \lambda \implies \frac{\lambda}{a} = \frac{\sqrt{3}}{4}$.For the first minimum $(n = 1)$,the condition is $a \sin 	heta_1 = 1 \lambda$.$\sin 	heta_1 = \frac{\lambda}{a} = \frac{\sqrt{3}}{4}$.$\sin 	heta_1 \approx \frac{1.732}{4} = 0.433$.$	heta_1 = \arcsin(0.433) \approx 25.6^{\circ}$.Rounding to the nearest integer,$	heta_1 \approx 25^{\circ}$.

Similar Questions

If we observe the single slit Fraunhofer diffraction with wavelength $\lambda$ and slit width $e$,the width of the central maxima is $2\theta$. On decreasing the slit width for the same $\lambda$,what happens to $\theta$?

Yellow light is used in a single slit diffraction experiment with a slit width of $0.6 \, mm$. If the yellow light is replaced by $X$-rays,then the pattern will reveal:

$A$ monochromatic light of wavelength $6000 \text{ Å}$ is incident on a single slit of width $0.01 \text{ mm}$. If the diffraction pattern is formed at the focus of a convex lens of focal length $20 \text{ cm}$, the linear width of the central maximum is: (in $\text{ mm}$)

Angular width of the central maximum of a diffraction pattern due to a single slit does not depend upon:

The half angular width of the central maxima in the Fraunhofer diffraction due to a slit of width $\frac{1200}{\sqrt{2}} \ \mu m$ is $45^o$. Then the wavelength of the light is ...... $\mu m$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module