Physics - Wave Optics Question with Solution | TestHub

The displacement of fringes due to the introduction of a glass plate of thickness $t$ and refractive index $\mu$ is given by

$y=\frac{D}{d}(\mu -1)t$

For the first plate with refractive index ${\mu }_1=1.44$, the displacement is

$y=\frac{D}{d}(1.44-1)t=0.44\frac{D}{d}t$

For the second plate with refractive index ${\mu }_2=1.66$ and the same thickness $t$, the new displacement $y^{\prime }$ is

$y^{\prime }=\frac{D}{d}(1.66-1)t=0.66\frac{D}{d}t$

Taking the ratio of the two displacements, we get

$\frac{y^{\prime }}{y}=\frac{0.66}{0.44}=\frac{3}{2}$

$y^{\prime }=\frac{3y}{2}$

Answer: $\frac{3y}{2}$