In the diffraction pattern due to a single slit of width α at the first minimum is observed at the angle 30 degree when light of wavelength 5000a is incident on the clicked the first secondary maximum is observed at an angle of
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=> sin^-1 [ 3/ 4 ]
Explanation:
As the first minimum is observed at the angle of 30° in a diffraction pattern due to a single slit of width a.
i.e n = 1, = 30°
According to Bragg's law of diffraction,
=> a sinѲ = n λ
=> a sin 30° = ( 1 ) λ ...[n = 1 ]
=> a = 2 λ _[i] ... { ∵ sin 30° = 1/2 }
For Ist secondary maxima
=> a sinѲ1 = 3λ / 2
=> sinѲ1 = 3λ / 2a _[ii]
Substitute value of a from Eq [i] and Eq [ii] we get,
=> sinѲ1 = 3 λ/ 4λ
=> sinѲ1 = 3/4
=> Ѳ1 = sin^-1 [ 3/4 ]
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