Question

In YDSE, the light source is red light of wavelength 700 nm. When a thin glass plate of refractive index 1.5 is placed in front of one of the slits then the central bright fringe shifts by ${10}^{-3}$ cm, the position previously occupied by the 5th bright fringe. Find the thickness of the plate in micrometers.___

Answer 1

$(S_{1}P{)}_{opt}=(S_{2}P{)}_{opt}{S}_{1}P-t+\mu t=S_{2}P(\mu -1)t=(S_{2}P-S_{1}P)\left(dsin\theta \right)=(\mu -1)t\frac{dy}{D}=(\mu -1)t\frac{d}{D}\left[\frac{5\lambda D}{d}\right]=(\mu -1)t(\mu -1)t=5\lambda \left(0.5\right)t=\left(5\right)700\times {10}^{-3}\mu mt=\frac{50}{5}\times 700\times {10}^{-3}\mu mt=7\mu m$