Question

Monochromatic light of wavelength $400nm$ and $560nm$ are incident simultaneously and normally on double slits apparatus whose slits separation is $0.1mm$ and screen distance is $1m$. Distance between areas of total darkness will be:

• A. $4mm$
• B. $5.6mm$
• C. $14mm$
• D. $28mm$

Answer 1

The correct option is D $28mm$

For $\lambda =400$mm

fringe width

$\beta =\frac{\lambda D}{d}=\frac{400\times 1\times 10\times 1000}{1\times {10}^6}$

$=4$mm

For $\lambda =560$mm

$\beta =\frac{\lambda D}{d}=5.6$mm

$LCM$ of both fringe width will give combined fringe width which is also the distance between $2$ minima .

$LCM4,5,6=28$mm