Question

Interference fringes are produced by a double-slit experiment and a piece of plane parallel glass refractive index $1.5$ is interposed in one of the interfering beams. If the fringes are displaced through $30$ fringe widths for light of wavelength $6\times {10}^{-5}cm$, if the thickness of the plate is $3.6\times {10}^{-X}cm$. Find X?

Answer 1

We know,

the path difference due to the glass plate,$\Delta x=(\mu -1)t=(1.5-1)t=0.5t$Δx=(μ−1)t=(1.5−1)t=0.5t

Due to this plate, fringes are displaced through 30 fringe width.

$\therefore \Delta x=30\lambda$

$or,0.5t=30\times 6\times {10}^{-5}cm$

or,0.5t=5×7×10−7m

Therefore, thickness of the glass plate, $t=3.6\times {10}^{-3}cm$t=7×10−6m

But given thickness of glasss plate is $3.6\times {10}^{-X}cm$Xμm=X×10−6m

Hence X=3 is the answer.