Understanding How Bodies Interact with Radiation

When radiation falls on a body, it can interact with the body in three main ways:

• Absorption: The body takes in the energy of the radiation.
• Reflection: The radiation bounces off the surface of the body.
• Transmission: The radiation passes through the body.

The total incident radiation must be accounted for by these three processes. We can represent this with the equation:

\( \alpha + \rho + \tau = 1 \)

Where:

• \( \alpha \) is the absorptivity (fraction absorbed).
• \( \rho \) is the reflectivity (fraction reflected).
• \( \tau \) is the transmissivity (fraction transmitted).

Defining Different Types of Bodies Based on Radiation Interaction

Different types of bodies are defined based on how they interact with incident radiation, specifically regarding their absorptivity, reflectivity, and transmissivity.

• White body: A body that reflects all the incident radiation. For an ideal white body, reflectivity \( \rho = 1 \), and absorptivity \( \alpha = 0 \), transmissivity \( \tau = 0 \). This means no radiation is absorbed or transmitted.

• Opaque body: A body that transmits none of the incident radiation. For an opaque body, transmissivity \( \tau = 0 \). The incident radiation is either absorbed or reflected (\( \alpha + \rho = 1 \)). Examples include most solid objects like metals, wood, and ceramics.

• Gray body: A gray body is defined as a body whose absorptivity (\( \alpha \)), reflectivity (\( \rho \)), and transmissivity (\( \tau \)) are constant for all wavelengths and temperatures. Unlike an ideal black body, \( \alpha \), \( \rho \), and \( \tau \) are between 0 and 1, but constant. For an opaque gray body, \( \tau = 0 \) and \( \alpha + \rho = 1 \), with \( \alpha \) and \( \rho \) constant (between 0 and 1, not equal to 0 or 1).

• Black body: An ideal body that absorbs all incident radiation, regardless of wavelength or direction. For a black body, absorptivity \( \alpha = 1 \), reflectivity \( \rho = 0 \), and transmissivity \( \tau = 0 \). A black body is a perfect absorber and also a perfect emitter of thermal radiation at a given temperature.

Identifying the Body with No Transmitted Radiation

The question asks for a body where no incident radiation is transmitted through it. Looking at the definitions above, the condition "no incident radiation is transmitted" means the transmissivity (\( \tau \)) is zero.

• A white body has \( \tau = 0 \).
• An opaque body has \( \tau = 0 \).
• An opaque gray body has \( \tau = 0 \).
• A black body has \( \tau = 0 \).

However, the fundamental definition of an opaque body is precisely a body that does not transmit radiation. White bodies and black bodies are specific types of opaque bodies (one that reflects everything, one that absorbs everything). A gray body can be opaque if its transmissivity is zero while having constant, non-zero absorptivity and reflectivity. The most general term among the options that fits the description "When no incident radiation is transmitted through the body" is an opaque body.

Therefore, a body through which no incident radiation is transmitted is called an opaque body.