A light source with a wavelength of 5000 , ma | vedclass

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(C) For a single-slit diffraction pattern,the position of the $n^{th}$ minimum is given by the formula: $x_n = \frac{n \lambda D}{a}$,where $a$ is the

Vedclass · Accepted Answer

$0.2$

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(C) For a single-slit diffraction pattern,the position of the $n^{th}$ minimum is given by the formula: $x_n = \frac{n \lambda D}{a}$,where $a$ is the slit width.Given:Wavelength $\lambda = 5000 \, \mathring A = 5000 	imes 10^{-10} \, m = 5 	imes 10^{-7} \, m$.Distance of the first minimum $x_1 = 5 \, mm = 5 	imes 10^{-3} \, m$.Distance between slit and screen $D = 2 \, m$.Order $n = 1$.Substituting these values into the formula:$5 	imes 10^{-3} = \frac{1 	imes (5 	imes 10^{-7}) 	imes 2}{a}$$a = \frac{10 	imes 10^{-7}}{5 	imes 10^{-3}}$$a = 2 	imes 10^{-4} \, m = 0.2 	imes 10^{-3} \, m = 0.2 \, mm$.Therefore,the width of the slit is $0.2 \, mm$.

Similar Questions

Two slits are made $1 \; mm$ apart and the screen is placed $1 \; m$ away. What should the width of each slit be to obtain $10$ maxima of the double-slit pattern within the central maximum of the single-slit pattern (in $; mm$)? Blue-green light of wavelength $500 \; nm$ is used.

If the measured angular separation between the second minimum to the left of the central maximum and the third minimum to the right of the central maximum is $30^{\circ}$ in a single slit diffraction pattern recorded using $628 \ nm$ light,then the width of the slit is . . . . . . $\mu m$.

In a single slit diffraction experiment,the width of the slit is doubled. Which one of the following statements is correct?

$A$ slit of width $a$ is illuminated by red light of wavelength $6500 \, \mathring{A}$. The first minimum will fall at $\theta = 30^{\circ}$ if $a$ is equal to:

$A$ single slit of width $0.1\, mm$ is illuminated by a parallel beam of light of wavelength $6000\, \mathring{A}$ and diffraction bands are observed on a screen $0.5\, m$ from the slit. The distance of the third dark band from the central bright band is ........ $mm$.

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