Question

In a Young's double slit set-up, light from a laser source falls on a pair of very narrow slits separated by $1.0$ micrometer and bright fringes separated by $1.0$ millmeter are observed on a distant screen. It the frequency of the laser light is doubled, what will be the separation of the bright fringes?

• A. $0.25mm$
• B. $0.5mm$
• C. $1.0mm$
• D. $2.0mm$

Answer 1

The correct option is B $0.5mm$

Fringe width $\beta =\frac{\lambda D}{d}$

where $\lambda =\frac{c}{\nu }$

$⟹$ $\beta \propto \frac{1}{\nu }$

Given : $\beta =1mm$ ${\nu }^{\prime }=2\nu$

$\therefore$ $\frac{{\beta }^{\prime }}{\beta }=\frac{\nu }{2\nu }$

Or $\frac{{\beta }^{\prime }}{1}=\frac{1}{2}$

$⟹$ ${\beta }^{\prime }=0.5mm$