Two wavelengths 590 nm and 596 nm of sodium | vedclass

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(A) The condition for the $n^{th}$ secondary maximum in a single slit diffraction pattern is given by $\sin 	heta = (2n + 1) \frac{\lambda}{2a}$.For

Vedclass · Accepted Answer

$7.5 	imes 10^{-6} \ m$

Vedclass · Answer

(A) The condition for the $n^{th}$ secondary maximum in a single slit diffraction pattern is given by $\sin 	heta = (2n + 1) \frac{\lambda}{2a}$.For the first secondary maximum $(n = 1)$,$\sin 	heta = \frac{3\lambda}{2a}$.Since the angle $	heta$ is very small,$\sin 	heta \approx 	an 	heta = \frac{x}{D}$,where $x$ is the distance from the central maximum and $D$ is the distance to the screen.Thus,$x = \frac{3\lambda D}{2a}$.The separation between the positions of the first secondary maxima for two wavelengths $\lambda_1$ and $\lambda_2$ is $\Delta x = \frac{3D}{2a} (\lambda_2 - \lambda_1)$.Given: $\lambda_1 = 590 	imes 10^{-9} \ m$,$\lambda_2 = 596 	imes 10^{-9} \ m$,$D = 2 \ m$,$a = 2.4 	imes 10^{-3} \ m$.Substituting the values:$\Delta x = \frac{3 	imes 2 	imes (596 - 590) 	imes 10^{-9}}{2 	imes 2.4 	imes 10^{-3}}$$\Delta x = \frac{6 	imes 6 	imes 10^{-9}}{4.8 	imes 10^{-3}} = \frac{36 	imes 10^{-9}}{4.8 	imes 10^{-3}} = 7.5 	imes 10^{-6} \ m$.

Similar Questions

$A$ 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 ........ $mm$.

In a diffraction experiment from a single slit,the angular width of the central maximum does $NOT$ depend upon:

$A$ screen is placed $0.5 \,m$ away from a single slit which is illuminated by a monochromatic light of wavelength $6000 \text{ Å}$. If the distance between the first and third minima in the diffraction pattern on the screen is $3 \,mm$, then the slit width is: (in $\,mm$)

$A$ narrow slit of width $2 \, mm$ is illuminated by monochromatic light of wavelength $500 \, nm$. The distance between the first minima on either side on a screen at a distance of $1 \, m$ is ........ $mm$.

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