Sodium light of wavelengths 650 nm and 655 nm is used to study diffraction at a single slit of apert

Question

Sodium light of wavelengths 650 nm and 655 nm is used to study diffraction at a single slit of aperture 0.5 mm . The distance between the slit and the screen is 2.0 m . The separation between the positions of the first maxima of diffraction pattern obtained in the two cases is _______ $	imes 10^{-5} \mathrm{~m}$.\

Professor PC Thomas Classes · Answer

(3) : $\lambda_{1}=650 \mathrm{~nm}, \lambda_{2}=655 \mathrm{~nm}$, $a=0.5 \mathrm{~mm}, D=2 \mathrm{~m}$\ For diffraction, $a \sin 	heta=(2 n+1) \lambda / 2$\ For $n=1$\ $\sin 	heta=\frac{3}{2} \frac{\lambda}{a}=\frac{y}{D} ; y=\frac{3 \lambda D}{2 a}$\ $y_{2}-y_{1}=\frac{3 D}{2 a}\left(\lambda_{2}-\lambda_{1}ight)$\ $y_{2}-y_{1}=\frac{3 	imes 2}{2 	imes 0.5 	imes 10^{-3}}(655-650) 	imes 10^{-9}$\ $y_{2}-y_{1}=3 	imes 10^{-5} \mathrm{~m}$