Physics - Wave Optics Question with Solution | TestHub

Before introducing the glass plate, the central maximum has zero path difference and maximum intensity.

When a glass plate of thickness $t$ and refractive index $\mu$ is introduced in one of the paths, the path difference at the original central position becomes $\Delta x=(\mu -1)t$.

For the intensity at this position to remain unchanged, it must continue to be a maximum.

The condition for maximum intensity (constructive interference) is $\Delta x=n\lambda$, where $n=1,2,3,\dots$

For the minimum thickness of the glass plate, we take $n=1$.

$(\mu -1)t=\lambda$

Substituting the given refractive index $\mu =1.5$:

$(1.5-1)t=\lambda$

$0.5t=\lambda$

$t=2\lambda$