Question

The Young's double slit experiment is performed with blue light and green light of wavelength $4360\dot{A}$ and $5460\dot{A}$ a respectively. If X is the distance of $4^{th}$ maxima, from the central one, then:

• A. $X_{blue}=X_{green}$
• B. $X_{blue}>X_{green}$
• C. $X_{blue}<X_{green}$
• D. $\frac{X_{blue}}{X_{green}}=\frac{5460}{4360}$

Answer 1

The correct option is C $X_{blue}<X_{green}$

Width of bands $\propto \lambda$
${\lambda }_b<{\lambda }_g$ $\therefore$ bands become narrower as wavelength decreases.
$X_{blue}=\frac{4D\times {\lambda }_b}{d},X_{green}=\frac{4D{\lambda }_g}{d}$
$\frac{X_{blue}}{X_{green}}=\frac{{\lambda }_b}{{\lambda }_g}=\frac{4360}{5460},X_{blue}<X_{green}$