A slit of width a is illuminated by monochromatic light of wavelength 650 mm at normal incidence calculate the value of a when
(a). The first minimum falls at an angle of diffraction of `30^(@)`
(b). The first maximum falls at an angle of diffraction of `30^(@)`.

Explanation

(a). For first minimum `sintheta_(1)=(lamda)/(a)`
`thereforea=(lamda)/(sintheta_(1))=(650xx10^(-9))/(sin30^(@))=(650xx10^(-9))/(0.5)=1.3xx10^(-6)m`
(b). For first maximum `sintheta_(1)=(3lamda)/(2a)`
`thereforea=(3lamda)/(2sintheta)=(3xx650xx10^(-9))/(2xx0.5)=1.95xx10^(-6)m`