Question

In a Young double slit experiment, $12$ fringes are observed to be formed in a certain segment of the screen when light of wavelength $600\text{nm}$ is used. If the wavelength of the light is changed to $400\text{nm}.$ The number of fringes observed in the same segment of the screen is (integer only)

Answer 1

Fringe width,

$\beta =\frac{\lambda D}{d}\Rightarrow \beta \propto \lambda$

When the wavelength is decreased from $600\text{nm}$ to $400\text{nm},$ fringe width will also decrease by a factor of $\frac{4}{6}$ (or) $\frac{2}{3}.$

Hence, the number of fringes in the same segment will increase by a factor of $\frac{3}{2}.$

$\therefore$ The number of fringes observed in the same segment $=12\times \frac{3}{2}=18$