Question

The central fringe of the interference pattern produced by light of wavelength $6000\stackrel{o}{A}$ is found to shift to the position of $4^{th}$ bright fringe after a glass plate of refractive index $1.5$ is introduced in path of one of beams. The thickness of the glass plate would be

• A. $4.8\mu \text{m}$
• B. $8.23\mu \text{m}$
• C. $14.98\mu \text{m}$
• D. $3.78\mu \text{m}$

Answer 1

The correct option is A $4.8\mu \text{m}$

Shift in fringe pattern $=\frac{4\lambda D}{d}$
Also shift due to glass plate $=\frac{(\mu -1)tD}{d}$

$\frac{4\lambda D}{d}$ $=\frac{(\mu -1)tD}{d}$

$t=\frac{4\lambda }{\mu -1}=\frac{4\times 6000\times {10}^{-10}}{1.5-1}\text{m}$

$t=8\times 6\times {10}^{-7}\text{m}=4.8\mu \text{m}$