Section (G) For Jee (main)
G-1 A slit of width 'a' is illuminated by light of wavelength 6000 $A^{o}$ For what value of 'a' will the :-
(i) First maximum fall at an angle of diffraction of $30^{o}$ ?
(ii) First minimum fall at an angle of diffraction $30^{o}$ ?

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Solution

Given,

Wavelength $λ = 6000 A^{o}$

Angle, $θ = 30^{o}$

Slit width $a$

(i) Constructive interference, $a sin θ = n λ$

For, first bright fringe(n=1) at angle $30^{o}$ , $a = \frac{λ}{sin 30^{o}} = \frac{6000 \times 10^{- 10}}{0.5} = 1.2 μ m$

(ii) Destructive interference $a sin θ = (n + \frac{1}{2}) λ$

For, first dark fringe(n=1) at angle $30^{o}$ , $a = \frac{1.5 λ}{sin 30^{o}} = \frac{6000 \times 10^{- 10}}{0.5} = 1.8 μ m$

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Section (G) For Jee (main)G-1 A slit of width 'a' is illuminated by light of wavelength 6000 Ao For what value of 'a' will the :-(i) First maximum fall at an angle of diffraction of 30o ? (ii) First minimum fall at an angle of diffraction 30o ?

Section (G) For Jee (main)
G-1 A slit of width 'a' is illuminated by light of wavelength 6000 $A^{o}$ For what value of 'a' will the :-
(i) First maximum fall at an angle of diffraction of $30^{o}$ ?
(ii) First minimum fall at an angle of diffraction $30^{o}$ ?