In double-slit experiment using light of wavelength 600 nm,
Question:

In double-slit experiment using light of wavelength 600 nm, the angular width of a fringe formed on a distant screen is 0.1º. What is the spacing between the two slits?

Solution:

Wavelength of light used, λ = 6000 nm = 600 × 10−9 m

Angular width of fringe, $\theta=0.1^{\circ}=0.1 \times \frac{\pi}{180}=\frac{3.14}{1800} \mathrm{rad}$

Angular width of a fringe is related to slit spacing (d) as:

$\theta=\frac{\lambda}{d}$

$d=\frac{\lambda}{\theta}$

$=\frac{600 \times 10^{-9}}{\frac{3.14}{1800}}=3.44 \times 10^{-4} \mathrm{~m}$

Therefore, the spacing between the slits is $3.44 \times 10^{-4} \mathrm{~m}$.