Question

In a Young's double slit experiment with slit separation $0.1\, mm$, one observes a bright fringe at angle $\frac{1}{40}$ rad by using light of wavelength $\lambda_1$. When the light of wavelength $\lambda_2$ is used a bright fringe is seen at the same angle in the same set up. Given that $\lambda_1$ and $\lambda_2$ are in visible range ($380\, nm$ to $740\, nm$), their values are :

• A. 380 nm, 500 nm
• B. 625 nm, 500 nm
• C. 380 nm, 525 nm
• D. 400 nm, 500 nm

Answer 1

Answer: (B)

Path difference = $d \; \sin \theta \approx \; d\theta$
$ = 0.1 \times \frac{1}{40} mm = 2500\, nm $
or bright fringe, path difference must be integral multiple of $\lambda$
$\therefore \; 2500 = n \lambda_1 = m \lambda_2$
$\therefore \; \lambda_1 = 625 , \lambda_2 = 500$ (from $m \,=\, 5$)
(for $n\, =\, 4$)