A silt of width `'a'` is illuminated by light of wavelength `6000 A^(@) FOR` What value of `'a` will the :-
(i) First maximum fall at an angle of diffraction of `30^(@)` ?
(ii) First minimum fall at an angle of diffracton `30^(@)` ?

Answer

`lambda=6000 A^(@)=6000xx10^(-10)m theta_(1)=30^(@),m=1`

Explanation

(i) For first maximum
`sintheta_(m)=((m+1/2)lambda)/(a)`
`sintheta_(1)=(3lambda)/(2a)`
or `a=(3lambda)/(2sintheta_(1))=(3xx6xx10^(-7))/(2xxsin 30^(@))`
(ii) For first minimum
`sintheta_(m)=(mlambda)/(a)`
or `sin theta_(1)=(lambda)/(a)`
`a=(lambda)/(sintheta_(1))`
`a=(6xx10^(-7))/(sin30^(@))`
`A=1.2xx10^(-6)m`