In Young's double-slit experiment,the distanc | vedclass

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(D) The condition for the $n^{th}$ bright fringe in Young's double-slit experiment is given by $x = \frac{n \lambda D}{d}$.Here,$x = 10^{-3} \, m$,$D

Vedclass · Accepted Answer

$8000$

Vedclass · Answer

(D) The condition for the $n^{th}$ bright fringe in Young's double-slit experiment is given by $x = \frac{n \lambda D}{d}$.Here,$x = 10^{-3} \, m$,$D = 2.5 \, m$,and $d = 2 	imes 10^{-3} \, m$.Rearranging for wavelength $\lambda$,we get $\lambda = \frac{xd}{nD}$.Substituting the values: $\lambda = \frac{10^{-3} 	imes 2 	imes 10^{-3}}{n 	imes 2.5} = \frac{2 	imes 10^{-6}}{2.5n} = \frac{0.8 	imes 10^{-6}}{n} = \frac{8000}{n} \, \mathring{A}$.For $n=1$,$\lambda = 8000 \, \mathring{A}$.For $n=2$,$\lambda = 4000 \, \mathring{A}$.For $n=3$,$\lambda \approx 2666.67 \, \mathring{A}$.Since the given range is $2000 \, \mathring{A}$ to $9000 \, \mathring{A}$,both $8000 \, \mathring{A}$ and $4000 \, \mathring{A}$ are valid solutions. Given the options,$8000 \, \mathring{A}$ is the correct choice.

Similar Questions

The fringe width in a $YDSE$ pattern is $2.4 \times 10^{-4} \, m$ when red light of wavelength $6400 \, \mathring{A}$ is used. How much will it change if blue light of wavelength $4000 \, \mathring{A}$ is used?

In Young's double-slit experiment,which of the following statements is correct?

$A$ Young's double-slit experiment uses a monochromatic source. The shape of the interference fringes formed on a screen is

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