# Problem on thermal radiation and lenses

• phantomvommand
In summary, when an object is at a far distance from a lens, its image is formed at the focus of the lens. To calculate the diameter of the image, we can use the hint that the angular diameter of the object and image are equal. The angular diameter is the angle subtended at the observer. This means that the diameter of the image will be equal to the diameter of the object when viewed from the same distance. The fact that the lens diameter is 100mm can be useful in determining the size of the image formed.

#### phantomvommand

Homework Statement
Relevant Equations
P (rad) = sigma e0 T^4
At long distances, images due to convex lenses are formed at the foci.

I know that the Sun is at a very far distance from the lens, so I assume the rays are parallel and the image is formed at the focus (500mm away from the centre of the lens).
How do I calculate the diameter of the image?
The hint to solving this problem says that "The angular diameters of object and image are equal". What is the "angular diameter", and what does the hint mean? If the light rays intersect at a focal point, how can there even be a diameter? Furthermore, how is the fact that the lens diameter = 100mm useful?

I am quite confused by this question, any help is appreciated. Thank you!

phantomvommand said:
Homework Statement:: Please see the attached photo
Relevant Equations:: P (rad) = sigma e0 T^4
At long distances, images due to convex lenses are formed at the foci.

View attachment 279679
I know that the Sun is at a very far distance from the lens, so I assume the rays are parallel and the image is formed at the focus (500mm away from the centre of the lens).
How do I calculate the diameter of the image?
The hint to solving this problem says that "The angular diameters of object and image are equal". What is the "angular diameter", and what does the hint mean? If the light rays intersect at a focal point, how can there even be a diameter? Furthermore, how is the fact that the lens diameter = 100mm useful?

I am quite confused by this question, any help is appreciated. Thank you!
A ray arriving from a point at one edge of the sun, as observed from Earth, is not quite parallel with a ray from the opposite edge, so they will not focus at the same point.
OTOH, rays from one point on the sun arriving at different points of the lens are effectively parallel, so do focus at the same point.
As a result, an actual image of the sun is produced, spots and all.

haruspex said:
A ray arriving from a point at one edge of the sun, as observed from Earth, is not quite parallel with a ray from the opposite edge, so they will not focus at the same point.
OTOH, rays from one point on the sun arriving at different points of the lens are effectively parallel, so do focus at the same point.
As a result, an actual image of the sun is produced, spots and all.

phantomvommand

## 1. What is thermal radiation?

Thermal radiation is a type of electromagnetic radiation that is emitted by any object with a temperature above absolute zero. It is caused by the movement of charged particles within the object and can be felt as heat.

## 2. How does thermal radiation affect lenses?

Thermal radiation can cause lenses to expand or contract, which can change their shape and affect their ability to focus light. This is known as thermal lensing and can be a problem in high-power laser systems.

## 3. What is the Stefan-Boltzmann law?

The Stefan-Boltzmann law is a fundamental law of physics that describes the relationship between the temperature of an object and the amount of thermal radiation it emits. It states that the total energy radiated per unit surface area of a black body is proportional to the fourth power of its absolute temperature.

## 4. How does thermal radiation impact the Earth's climate?

Thermal radiation plays a crucial role in the Earth's climate by trapping heat from the sun and keeping the planet warm enough to sustain life. However, an increase in greenhouse gases, such as carbon dioxide, can lead to an enhanced greenhouse effect and cause the Earth's temperature to rise, leading to climate change.

## 5. Can thermal radiation be harnessed for energy?

Yes, thermal radiation can be harnessed for energy in the form of solar power. Solar panels use photovoltaic cells to convert thermal radiation from the sun into electricity. This renewable energy source is becoming increasingly popular as a sustainable alternative to fossil fuels.