For what distance is ray optics a good approximation when the aperture is 2 mm wide and the wavelength is 400 nm?
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 10 m
A beam passing through an aperture of size \( a \) spreads by diffraction. The spreading becomes comparable to the size of the aperture at the Fresnel distance
\( \displaystyle z_F = \frac{a^{2}}{\lambda} \)
Up to distances of the order of \( z_F \) the spreading is small and the beam travels in straight lines, so ray optics is a good approximation.
\( a = 2\,\mathrm{mm} = 2\times10^{-3}\,\mathrm{m} \)
\( \lambda = 400\,\mathrm{nm} = 4\times10^{-7}\,\mathrm{m} \)
\( \displaystyle z_F = \frac{(2\times10^{-3})^{2}}{4\times10^{-7}} = \frac{4\times10^{-6}}{4\times10^{-7}} = 10\,\mathrm{m} \)
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 – …
