Question

Laser light of wavelength $630nm$ incident on a pair of slits produces an interference pattern in which the bright fringes are separated by $8.1mm$. A second light produces an interference pattern in which the fringes are separated by $7.2mm$. Then the wavelength of the second light will be

• A. $500nm$
• B. $560nm$
• C. $600nm$
• D. $660nm$

Answer 1

The correct option is B $560nm$

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

In the question, since the slits remain the same, $D$ and $d$ don't change.

Thus, $\frac{{\beta }_2}{{\beta }_1}=\frac{{\lambda }_2}{{\lambda }_1}$
$\Rightarrow \frac{7.2mm}{8.1mm}=\frac{{\lambda }_2}{630nm}$
$\Rightarrow {\lambda }_2=560nm$