What is the distance that a beam of light of wavelength 500 nm can travel without significant broadening, if the diffracting aperture is 3 mm wide?
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 18 m
A beam from an aperture of width \( a \) spreads by diffraction through an angle of about \( \lambda/a \). Ray optics holds until this spreading becomes comparable to the aperture, which happens at the Fresnel distance \( z_F = \frac{a^{2}}{\lambda} \).
\( \displaystyle z_F = \frac{a^{2}}{\lambda} = \frac{(3\times10^{-3}\,\mathrm{m})^{2}}{500\times10^{-9}\,\mathrm{m}} = \frac{9\times10^{-6}}{5\times10^{-7}}\,\mathrm{m} = 18\,\mathrm{m} \)
Note: This question is from the pre-rationalised NCERT book (2022-23). The topic was removed from the latest NCERT book (2026-27), and it also appears to be out of the CUET 2026 syllabus.
NCERT (Pre-rationalised edition, 2022-23):
The Validity of Ray Optics – …
