Question

In the ideal double-slit experiment, when a glass-plate (refractive index 1.5) of thickness t is introduced in the path of one of the interfering beams (wavelength $\lambda$), the intensity at the position where the central maximum occurred previously remains unchanged. The minimum thickness of the glass-plate is

• A. 2$\lambda$
• B. $\frac{2 \lambda}{3}$
• C. $\frac{\lambda}{3}$
• D. $\lambda$

Answer 1

The Correct Option is A

Path difference due to slab should be integral multiple of $\lambda$ or
$\hspace10mm ? x=n \lambda \, or \, (\mu-1)t=n \lambda$ n = 1,2,3,..
or $\hspace20mm t=\frac{n \lambda}{\mu-1}$
For minimum value of t, n = 1
$\therefore \hspace20mm t=\frac{\lambda}{\mu-1}=\frac{\lambda}{1.5-1}=2 \lambda$