Question

In young's experiment, the source of red light of wavelength $7\times {10}^{-7}m$. When a thin glass plate of refractive index $1.5$ at this wavelength is put in the path of one of the interfering beams, the central fringe shifts by ${10}^{-3}m$ to the position previously occupied by the 5th bright fringe. If the thickness of the plate is $X\mu m$
Find X?

Answer 1

Given:

Wavelength of red light, ${\lambda }_{red}=7\times {10}^{-7}m$

We know,

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

Due to this slab, 5 red fringes have been shifted upwards.

$\therefore \Delta x=5{\lambda }_{red}$

$or,0.5t=5\times 7\times {10}^{-7}m$

Therefore, thickness of the glass slab$t=7\times {10}^{-6}m$

But given thickness of glasss slab is $X\mu m=X\times {10}^{-6}m$

Hence $X=7$ is the answer.