How is the spacing between fringes in a double slit experiment affected if :

(i)

the slits separation is increased,

(ii)

the colour of light used is changed from red to blue,

(iii)

the whole apparatus is submerged in a oil of refractive index $\displaystyle 1.2$ ? Justify your anwer in each case.

Spacing between fringes in Young's doubles slit experiment $$ \beta=\frac{\lambda D}{d}$\displaystyle 1$) $\displaystyle \beta$ decreases as $\displaystyle d$ increases as $\displaystyle \beta \propto \frac{1}{d}$ $\displaystyle 2$) $\displaystyle \lambda_{\text {blue }}<\lambda_{\text {red }}$ as $\displaystyle \beta \propto \lambda$ ∴ fringe width decreases. $\displaystyle 3$) $\displaystyle \beta^{\prime}=\frac{\beta}{\mu} \quad \therefore \beta$ decreases as $\displaystyle \mu>1[\therefore \mu=1.2]$