Question

In YDSE experiment slits are illuminated by light of consisting two wavelengths ${\lambda }_1=600nm$ and ${\lambda }_2=400nm$. Slit separation is 0.5 mm and screen is 2 m away from slits. Separation between $2^{nd}$ order minima of two wavelengths in mm is (Write upto two digits after the decimal point.)

Answer 1

Position of minima is $y=(2n-1)\frac{\lambda D}{2d}$
For 2nd minima $y_2=\frac{3\lambda D}{2d}$$y_2\text{'}=\frac{3\lambda \text{'}D}{2d}\Delta y=\frac{3D}{2d}(\lambda \text{'}-\lambda )=\frac{3\times 2\times (600-400)\times {10}^{-9}}{2\times 0.5\times {10}^{-3}}=1.2\times {10}^{-3}m=1.20mm$