When Is Reflection Significant? Wavelength vs. Object Size The strength of EM reflection from a target depends on the relation between wavelength and object dimensions. Reflection from the object is significant only when the wavelength is:

Introduction / Context:
Target detectability in radar and general scattering problems depends on the ratio of object size to wavelength. This question asks which relationship makes reflections strong enough to be significant for measurement.

Given Data / Assumptions:

• Simple monostatic reflection from an object in free space.
• No resonant cavity effects; we are focused on size vs. wavelength scaling.
• “Significant” means the scattered field is large compared with background/noise.

Concept / Approach:

Scattering theory distinguishes three regimes: Rayleigh (object ≪ wavelength), resonance (object ≈ wavelength), and optical (object ≫ wavelength). For a given object, as the wavelength becomes much smaller than the object’s size, geometric optics applies and reflections are strong (large radar cross section). When the wavelength is much larger than the object (Rayleigh), scattering is weak and falls rapidly with decreasing size relative to wavelength.

Step-by-Step Solution:

Verification / Alternative check:

Radar cross-section approximations grow with physical cross-section as λ decreases relative to dimensions, supporting the “much smaller than the object” condition.

Why Other Options Are Wrong:

(A) leads to Rayleigh weak scattering; (C) can produce noticeable effects but “only when” is too restrictive compared with strong, reliable reflection in the λ ≪ size regime; (D) includes (A) which is incorrect; (E) is an arbitrary ratio without general validity.

Common Pitfalls:

Assuming resonance is required for detectability; large objects at high frequency can be easily detected without resonance.

Final Answer:

much smaller than the size of the object