Question

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

• A. $420\, nm$
• B. $560\, nm$
• C. $810\, nm$
• D. $980\, nm$

Answer 1

Answer: (B)

Here $\lambda_1 = 630 \,nm, β_1 = 8.1\, mm, β_2 = 7.2\, mm$
Fringe width, $\beta=\frac{D\lambda}{d}$
For constant $D$ and $d, β ∝ \lambda$
$\therefore \frac{\beta_{2}}{\beta_{1}}=\frac{\lambda_{2}}{\lambda_{1}}$
$\therefore \lambda_{2}=\frac{\beta_{2}}{\beta_{1}}\times\lambda_{1}=\frac{7.2\,mm}{8.1\,mm}\times630\,nm=560\,nm.$