Question

Using Young's double slit experiment, a monochromatic light of wavelength $5000\AA$ produces fringes of fringe width $0.5mm$. If another monochromatic light of wavelength $6000\AA$ is used and the separation between the slits is doubled, then the new fringe width will be:

• A. $0.3mm$
• B. $0.6mm$
• C. $1.0mm$
• D. $0.5mm$

Answer 1

The correct option is A $0.3mm$

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

when light of $5000$ Å is used;

$0.5=\frac{5000D}{d}$

$\Rightarrow \frac{D}{d}=\frac{0.5}{5000}$

when light of $6000$ Å is used and separation between slits is doubled;

$\beta {}^{\prime }=\frac{6000}{2}\times \frac{D}{d}$

$\beta {}^{\prime }=\frac{6000}{2}\times \frac{0.5}{5000}$

$\Rightarrow \beta {}^{\prime }=\frac{3}{10}=0.3mm$