In Young's double-slit experiment, monochromatic light of wavelength $600$ nm is used. The slit separation is $0.5$ mm and the screen is $1.0$ m away. Find the fringe width.
A$0.6$ mm
B$1.2$ mm
C$2.4$ mm
D$6.0$ mm
Answer & Solution
Correct answer: B. $1.2$ mm
$\beta = \dfrac{\lambda D}{d}$. Convert units to SI before substituting:
$\beta = \dfrac{(600 \times 10^{-9}\,\text{m}) \times (1.0\,\text{m})}{0.5 \times 10^{-3}\,\text{m}} = \dfrac{6 \times 10^{-7}}{5 \times 10^{-4}} = 1.2 \times 10^{-3}\,\text{m} = 1.2\,\text{mm}$.
A quick sanity check: fringe widths in classroom Young experiments are usually in the millimetre range, so the order of magnitude is right.
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