In double-slits experiment using light of wavelength 550 nm, the angular width of a fringe formed on a distant screen is 0.2°. What is the spacing between the two slits?
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 0.158 mm
In the double-slit experiment the angular width of a fringe is \( \theta = \lambda/d \), where d is the slit spacing. The angle must be in radians.
\( \displaystyle \theta = 0.2^\circ = 0.2\times\frac{\pi}{180} = 3.49\times10^{-3}\,\mathrm{rad} \)
\( \displaystyle d = \frac{\lambda}{\theta} = \frac{550\times10^{-9}\,\mathrm{m}}{3.49\times10^{-3}} \)
\( d \approx 1.58\times10^{-4}\,\mathrm{m} = 0.158\,\mathrm{mm} \)