Question 329: Waves Optics

Question

In Young's double slit experiment when a glass plate of refractive index 1.44 is introduced in the path of one of the interfering beams, the fringes are displaced by a distance '$$y$$'. If this plate is replaced by another plate of same thickness but of refractive index 1.66, the fringes will be displaced by a distance

Accepted Answer

As a glass plate is used in one of the paths,
$$\begin{aligned}
& y_1=\frac{\beta}{\lambda}(1.44-1) t \
& y_1=0.44 t 	imes \frac{\beta}{\lambda}
\end{aligned}$$
New displacement is:
$$\begin{aligned}
\mathrm{y}_2 & =\frac{\beta}{\lambda}(1.66-1) \mathrm{t} \
\mathrm{y}_2 & =0.66 \mathrm{t} 	imes \frac{\beta}{\lambda} \
\frac{\mathrm{y}_2}{\mathrm{y}_1} & =\frac{0.66}{0.44} \
	herefore \quad \mathrm{y}_2 & =\frac{3 \mathrm{y}}{2}
\end{aligned}$$

Answer

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

Answer

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

Answer

$$\frac{5 y}{4}$$

Answer

$$\frac{4 y}{5}$$

Waves Optics

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