Question

An aperture of size \(a\) is illuminated by a parallel beam of light of wavelength \(\lambda\). The distance at which ray optics has a good approximation is

• A. \(\frac{a^2}{\lambda}\)
• B. \(\frac{\lambda}{a^2}\)
• C. \(\frac{\lambda}{a}\)
• D. \(\frac{\lambda^2}{a}\)
• E. \(a^2 \lambda\)

Hint:

Ray optics works when aperture size is large compared to wavelength.

Answer 1

The Correct Option is A

Concept: Ray optics approximation is valid when diffraction effects are negligible.

Step 1: Understand condition for ray optics.
Diffraction becomes negligible when observation distance is much larger than Fresnel distance.

Step 2: Fresnel distance formula. \[ z = \frac{a^2}{\lambda} \]

Step 3: Interpretation.
For distances greater than this, wave effects diminish and ray optics holds.

Step 4: Conclusion. \[ \boxed{\frac{a^2}{\lambda}} \]