Problem 6 - Astronomy Journey to the Cosmic Frontier

Question

A body absorbs \(30 \%\) of the light that strikes it. What is the albedo of the body? What happens to the light striking the body that isn't absorbed?

Step-by-Step Solution

Answer

The albedo is 70%, and the non-absorbed light (70% of it) is reflected.

Step 1: Understand Albedo

Albedo is a measure of the reflectivity of a surface. It is the fraction of light or radiation that is reflected by a surface, typically a planet or moon, and is expressed as a percentage. It helps us understand how much light is absorbed versus reflected by a body.

Step 2: Calculate the Absorbed Light

Given that the body absorbs 30% of the incident light, this means that out of 100% of the incoming light, 30% is absorbed by the body.

Step 3: Determine the Reflected Light

Since the total light striking the body is 100%, and 30% of it is absorbed, the remaining 70% must be reflected. This is because light that is not absorbed is reflected, considering there are no other losses specified.

Step 4: Calculate the Albedo

Albedo is defined as the percentage of light that is reflected. Thus, the albedo of the body is the same as the percentage of light that is reflected away, which is 70%.

Step 5: Summarize the Outcome for Non-absorbed Light

The light that is not absorbed by the body, making up 70% of the total, is reflected away from the body. This is the fundamental concept of albedo.

Key Concepts

Light Absorption

Light absorption occurs when a body or surface takes in light energy. Instead of reflecting all light, some surfaces are better at absorbing it. When light hits an object, certain wavelengths are absorbed while others may be reflected or transmitted.

• Absorbed light can transfer heat to the absorbing body, increasing its temperature.
• The degree of absorption depends on the material and color of the surface—darker colors often absorb more light, thus more heat.
• If 30% of light is absorbed by a body, it directly means that 30% of the energy carried by the incoming light is retained by the body.

Understanding absorption helps us grasp why some surfaces feel warmer than others under the same lighting conditions.

Light Reflection

Light reflection is the process by which light bounces off the surface of an object rather than being absorbed. Reflection contributes significantly to what we observe:

• It determines the brightness and visibility of the object under a light source.
• For example, a mirror showcases perfect reflection, where most of the incoming light is reflected with minimal absorption.
• Surfaces that reflect more light tend to appear brighter and less warm compared to surfaces with high absorption.

The amount of light reflected is directly tied to albedo. In the given problem, 70% of the light is reflected, explaining why that is the albedo value.

Reflectivity of Surfaces

Reflectivity describes how much light a surface can reflect compared to how much it absorbs. Surfaces can vary greatly in their reflectivity:

• Materials like metals, ice, and light-colored surfaces generally have high reflectivity, meaning they bounce back a large portion of incoming light.
• On the other hand, surfaces like asphalt or coal have low reflectivity and absorb more light.
• Albedo, as highlighted in the original problem, gives a numerical value to reflectivity. A higher albedo indicates a greater reflection capacity.

By understanding reflectivity, we can judge how surfaces contribute to their environment, particularly influencing temperature and energy efficiency.