In a diffraction pattern due to single slit of width 'a', the first minimum is observed at an angle of 30^ when the light of wavelength 5400 Å is incident on the slit. The first secondary maximum is observed at an angle of ( 30^ = 1 2 )

Step-by-step solution

For n ^ th secondary minimum, path difference =a _ n = n For n ^ th secondary maximum, path difference =a _n=(2 n+1) 2 For 1^ st minimum, a 30^ = For 2^ nd maximum, a _ n =(2+1) 2 = 3 2 Dividing equation (i) by equation (ii), ( 1 2 ) _n = 2 3 _n= ⁻¹ ( 3 4 )