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For an opaque surface, the absorptivity (α), transmissivity (τ) and reflectivity (ρ) are related by the equation:

  • A.\(\alpha+\rho=\tau\)
  • B.\(\rho+\alpha+\tau=0\)
  • C.\(\alpha+\rho=1\)
  • D.\(\alpha+\rho=0\)

Answer: C

For an opaque surface, \(\alpha+\rho=1\).

Radiation falling on any surface is absorbed, reflected or transmitted, so the three fractions add up to one:

\[ \alpha+\rho+\tau=1 \]

An opaque surface transmits nothing, so \(\tau=0\) and the relation reduces to \(\alpha+\rho=1\).

The fractions are each between 0 and 1, so their sum can never be zero, which rules out both options ending in 0. \(\alpha+\rho=\tau\) would mean the surface transmits as much as it absorbs and reflects together, which contradicts both the energy balance and the meaning of opaque.

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