Question

For an opaque body, coefficient of transmission is:
(A). Zero
(B). 1
(C). 0.5
(D). ∞

Answer 1

Hint: The coefficient of transmission is basically related to the amount of light that can pass through the body that we are talking about. If all light can pass through it, then its value is maximum whereas if no light can pass through it, its value should be minimum.

Complete step by step solution:

A wave of light is basically composed of waves and troughs carrying a certain amount of energy. When it is incident on an interface (boundary) between two media, it tries to pass from one medium to another but this transmission depends on the properties of the media under consideration. It may get completely absorbed, or partially absorbed. We understand transmission of light in terms of what we call the coefficient of transmission or transmittance. It is basically a number which tells us how much of the incident wave of light will be transmitted from one medium to another. Larger the transmission, bigger is the value of transmission coefficient.
Mathematically, we understand the coefficient of transmission in the following way. It is defined as the ratio of amount of energy transmitted to the amount of energy incident on the interface.
$$ \nu = \dfrac{{{E_t}}}{{{E_i}}} $$
where $\nu $ is the transmission coefficient, ${E_i}$ is the energy of the incident wave and
${E_t}$ is the energy of the transmitted wave.
As we know, an opaque body does not allow any amount of light to pass through it, which means that in the case of an opaque body, ${E_t}$ is zero. This means that whatever is the energy of the incident wave, the transmission coefficient for an opaque body is zero.
Hence, the correct answer to our question is option A.

Note: The student should remember the expression for coefficient of transmission. The ratio is with ${E_t}$ in numerator and ${E_i}$ in denominator. It’s not the other way around, which can lead to wrong answers of infinity. Since, an opaque body doesn’t allow any amount of light to pass through it; the coefficient cannot have any other value than 0.