A narrow slit of width 2 mm is illuminated w | vedclass

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

Question

(B) The condition for the $n^{th}$ minima in single-slit diffraction is given by $a \sin 	heta = n \lambda$,where $a$ is the slit width,$\lambda$ is

Vedclass · Accepted Answer

$0.5$

Vedclass · Answer

(B) The condition for the $n^{th}$ minima in single-slit diffraction is given by $a \sin 	heta = n \lambda$,where $a$ is the slit width,$\lambda$ is the wavelength,and $n$ is the order of the minima.For the first minima,$n = 1$,so $a \sin 	heta = \lambda$.Since the angle $	heta$ is very small,$\sin 	heta \approx 	an 	heta = \frac{y}{D}$,where $y$ is the distance from the central maximum and $D$ is the distance to the screen.Thus,$y = \frac{n \lambda D}{a}$.For the first minima $(n = 1)$,$y_1 = \frac{\lambda D}{a}$.The distance between the first minima on either side of the central maximum is $2y_1 = \frac{2 \lambda D}{a}$.Given: $a = 2 \ mm = 2 	imes 10^{-3} \ m$,$\lambda = 500 \ nm = 500 	imes 10^{-9} \ m$,$D = 1 \ m$.Substituting the values: $2y_1 = \frac{2 	imes 500 	imes 10^{-9} 	imes 1}{2 	imes 10^{-3}} = 500 	imes 10^{-6} \ m = 0.5 	imes 10^{-3} \ m = 0.5 \ mm$.

$A$ narrow slit of width $2 \ mm$ is illuminated with a monochromatic light of wavelength $500 \ nm$. If the distance between the slit and the screen is $1 \ m$,then the first minima are separated by a distance of: (in $mm$)

Similar Questions

Monochromatic light of wavelength $580 \,nm$ is incident on a slit of width $0.30 \,mm$. The screen is $2 \,m$ from the slit. The width of the central maximum is ........... $\times 10^{-3} \,m$.

Determine the angular separation between the central maximum and the first-order maxima of the diffraction pattern due to a single slit of width $0.25\, mm$ when light of wavelength $5890\,\mathring{A}$ is incident on it.

Light of wavelength $550\, nm$ falls normally on a slit of width $22.0 \times 10^{-5}\, cm$. The angular position of the second minima from the central maximum will be (in radians)

Assertion: The clouds in the sky generally appear to be whitish.
Reason: Diffraction due to clouds is efficient in equal measure at all wavelengths.

Vedclass Test Series

Exam Paper Generator

Online Exam Module