Question

Monochromatic light of wavelength $400$ nm and $560$ nm are incident simultaneously and normally on double slits apparatus whose slits separation is $0.1$ mm 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 $28mm$

$(2n+1){\lambda }_1=(2m+1){\lambda }_2$

$\frac{2n+1}{2m+1}=\frac{560}{400}=\frac{7}{5}$

$10n=14m+2$By inspection, for $m=2;n=3$

Also, $m=7;n=10$

$\therefore \Delta s=\frac{{\lambda }_{1}D}{2d}\left[\right(2n_2+1)-(2n_1+1\left)\right]=28mm$.