Question

A transparent paper (refractive index = 1⋅45) of thickness 0⋅02 mm is pasted on one of the slits of a Young's double slit experiment which uses monochromatic light of wavelength 620 nm. How many fringes will cross through the centre if the paper is removed?

Answer 1

Given:
Refractive index of the paper, μ = 1.45
The thickness of the plate, $t=0.02\mathrm{mm}=0.02\times {10}^{-3}\mathrm{m}$
Wavelength of the light, $\lambda =620\mathrm{nm}=620\times {10}^{-9}\mathrm{m}$
We know that when we paste a transparent paper in front of one of the slits, then the optical path changes by $\left(\mathrm{\mu }-1\right)t$.
And optical path should be changed by λ for the shift of one fringe.
∴ Number of fringes crossing through the centre is
$$\begin{gathered} n=\frac{\left(\mathrm{\mu }-1\right)t}{\lambda } \\ =\frac{\left(1.45-1\right)\times 0.02\times {10}^{-3}}{620\times {10}^{-9}} \\ =14.5 \end{gathered}$$

Hence, 14.5 fringes will cross through the centre if the paper is removed.