Saved Bookmarks
| 1. |
(a) In a single-slit diffraction experiment, a slit of width 'd' is illuminated by red light of wavelength 650 nm. For what value of 'd' will (i) the first minimum fall at an angle of diffraction of 30^(@) and (ii) the first maximum fall at an angle of diffraction of 30^(@) ? |
|
Answer» Solution :(a) (i) Here wavelength of light `l=650nm=6.5xx10^(-7)m`. As first minimum (n=1) falls at an angle of DIFFRACTION `theta=30^(@)`, hence `dsintheta=nlamda=(nlamda)/(sintheta)=(1xx6.5xx10^(-7))/(SIN30^(@))=(6.5xx10^(-7))/(0.5)=1.3xx10^(-6)m` ((II) As first maximum (n=1) falls at an angle of diffraction `theta=30^(@),` hence, (ii) As first maximum (n=1) falls at an angle of diffraction `theta=30^(@)`, hence, `dsintheta=(2n+1)(lamda)/(2)=((2n+1)lamda)/(2sintheta)=((2xx1+1)xx6.5xx10^(-7))/(2xxsin30^(@))=(3xx6.5xx10^(-7))/(2xx0.5)=1.95xx10^(-6)m`. (b) For central diffraction maximum whole wavefront CONTRIBUTES towards the intensity. however, for SUCCESSIVE diffraction maxima only `(1)/(3),(1)/(5),(1)/(7)`th part of the wavefront contributes towards the intensity of maxima. consequently intensity of successive maxima become less and lesser as compared to the central maximum. |
|