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  4. A thin plastic sheet of refractive index text1.6 is used to cover one of the slits, among the two slits, in a double-slit arrangement. The central point on the screen is now occupied by what would have been the 7t h bright fringe before the thin plastic sheet was used. If the wavelength of light is 600 nm , the thickness (in μm ) of the thin plastic sheet is

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Q. A thin plastic sheet of refractive index $\text{1.6}$ is used to cover one of the slits, among the two slits, in a double-slit arrangement. The central point on the screen is now occupied by what would have been the $7^{t h}$ bright fringe before the thin plastic sheet was used. If the wavelength of light is $600 \, nm$ , the thickness (in $μm$ ) of the thin plastic sheet is

NTA AbhyasNTA Abhyas 2020Wave Optics

Solution:

The change in path $=\left(\mu - 1\right)t$ . This path length change the position of bright fringe upto seventh bright fringe.
$t\left(\right. \mu - 1 \left.\right)=7\lambda $
$t=\frac{7\left(600 \times 10^{-9}\right)}{(1.6-1)}$
$=7\times 10^{- 6}m\Rightarrow 7μm$