The two slits are 1 mm apart from each other and illuminated with a light of wavelength $5 imes 10

Question

The two slits are 1 mm apart from each other and illuminated with a light of wavelength $5 	imes 10^{-7} \mathrm{~m}$. If the distance of the screen is 1 m from the slits, then the distance between third dark fringe and fifth bright fringe is\

Professor PC Thomas Classes · Answer

C)Given $\lambda=5 	imes 10^{-7} \mathrm{~m}, \mathrm{D}=1 \mathrm{~m}, \mathrm{~d}=1 \mathrm{~mm}$. Distance of nth bright fringe from the centre $=\frac{\mathrm{nD} \lambda}{\mathrm{d}}$\ Where $\mathrm{n}=1,2,3, \ldots$\ So the distance of $5^{	ext {th }}$ bright fringe $=\frac{5 \mathrm{D} \lambda}{\mathrm{d}}$\ Distance of nth fringe from the centre $=\left(\mathrm{n}-\frac{1}{2}ight) \frac{\mathrm{D} \lambda}{\mathrm{d}}$\ where $\mathrm{n}=1,2,3,4 \ldots$\ $3^{	ext {rd }}$ dark fringe $=\left(3-\frac{1}{2}ight) \frac{\mathrm{D} \lambda}{\mathrm{d}}=\frac{5}{2} \frac{\mathrm{D} \lambda}{\mathrm{d}}$\ $=\frac{5 	imes 1 	imes 5 	imes 10^{-7}}{1 	imes 10^{-3}}=12.5 	imes 10^{-4} \mathrm{~m}=1.25 \mathrm{~mm}$.\