Rayleigh criterion for surface smoothness

Steps:

• Visible light wavelengths range from approximately 400 nm (violet) to 700 nm (red).
• For a surface to appear smooth, surface bumps must be smaller than the shortest visible wavelength to prevent light scattering.
• The shortest wavelength is about 400 nm, so maximum bump size is just below this value.
• 350 nm approximates the upper limit for bumps that remain sub-wavelength across the visible spectrum.

Why B is correct:

• 350 nm is smaller than the minimum visible light wavelength (~400 nm), ensuring no diffraction or scattering makes the surface appear rough.

Why the others are wrong:

• A: 20 nm is far smaller than needed; surfaces can have larger bumps and still appear smooth.
• C: 720 nm exceeds the visible range upper limit (~700 nm), allowing scattering of red light.
• D: 5 μm (5000 nm) is much larger than all visible wavelengths, causing clear roughness via diffraction.

Final answer: B