# Spherical mirror area according to the amount of light

• ex3mist
In summary, Vidar is asking about how to calculate the amount of light that is focused in the mirror's focus point depending on the mirror's area and the amount of light emited by the source. He also wants to know if there is any loss of light when the light is reflected by another plain mirror to another point. He is also curious about the terms "focus point" and "energy per unit time."
ex3mist
Hello,
I need some information about spherical mirrors that I can't find in internet or this forum.
1. How to calculate the amount of light that is focused in the mirror's focus point depending on the mirror's area and the amount of light emited by the source?
2. If that light is reflected by another plain mirror to another point, is there any loss of light? I mean loss of efficiency.
The purpose of my questions is if I want certain amount of light, how can I calculate the spherical mirror's area and to take into account any losses?

Thanks!

Other than the surface area of the mirror all I think you need is how well the mirror reflects the light. There are no perfect mirrors and adding another to your optical system will always reduce the amount of light by at small amount. Or more if you use low quality mirrors.

Well, of course the quality of the mirror is very important, but I consider it would be used high quality mirrors. What bothers me most is is there an equation that defines the dependence between the area of the mirror and the amount of light in its focus point? If I want certain amount of light, how can I determine how big the mirror has to be?

ex3mist said:
Well, of course the quality of the mirror is very important, but I consider it would be used high quality mirrors. What bothers me most is is there an equation that defines the dependence between the area of the mirror and the amount of light in its focus point? If I want certain amount of light, how can I determine how big the mirror has to be?

How much energy per unit time do you want to deliver to an object at the focal point?

How much energy does your light source deliver to a unit area of the mirror per unit time?

Think about the physical significance of these two quantities for a moment, and it will be clear ho wto calculate the required area of the mirror from them.

@ ex3mist:
What do you need a spherical mirror for? Wouldn't it be better with a parabolic mirror instead? Parabolic mirrors do focus parallell incoming light into a single point. Spherical mirrors don't.

I ask because you mention focus point. A spherical mirror does not have a defined focus point, a parabolic mirror does.

Vidar

@Nugatory:
I just want an equation. If there is one... The source is the Sun. The light varies depending on the weather.

@Low-Q:
I'm not sure about the terms, maybe you're right. I just want to use Sun light and to focus it.

ex3mist said:
@Nugatory:
I just want an equation. If there is one... The source is the Sun. The light varies depending on the weather.

@Low-Q:
I'm not sure about the terms, maybe you're right. I just want to use Sun light and to focus it.
Isn't it approx 6 kW per square meter at equtor? Mayby I don't remember correctly.
Focus that energy into a square centimeter. You might get hurt in your fingertip if you put it there :-) The energy will still be approx 6 kW there - minus loss from the none-perfect mirror. The size of the spot depends on the size and distance of the sun, and what the focal length are. The focal length is the only possible variable. Sorry for not having an equation for you.

Vidar.

Thanks Vidar, I didn't know about the 6 kW per square meter. That gives me some ideas. Maybe that information is better. ;) Can I read more about it somewhere? Can you give a link, please?

Low-Q said:
Isn't it approx 6 kW per square meter at equtor? Mayby I don't remember correctly.
Focus that energy into a square centimeter. You might get hurt in your fingertip if you put it there :-) The energy will still be approx 6 kW there - minus loss from the none-perfect mirror. The size of the spot depends on the size and distance of the sun, and what the focal length are. The focal length is the only possible variable. Sorry for not having an equation for you.

Vidar.

That number is a little high - if I remember right, it's about 1kW per square meter below the atmosphere, and about 1.2kW per square meter in space (latitude doesn't matter, as long as the collector is directly facing the sun)

Quote from Wikipedia (I overrated that energy by some factor):
"The total amount of energy received at ground level from the sun at the zenith is 1004 watts per square meter, which is composed of 527 watts of infrared radiation, 445 watts of visible light, and 32 watts of ultraviolet radiation."

So there you go. Here is the link: http://en.wikipedia.org/wiki/Sunlight

Vidar

## 1. How is the area of a spherical mirror related to the amount of light it reflects?

The area of a spherical mirror is directly proportional to the amount of light it reflects. This means that the larger the mirror's surface area, the more light it will reflect.

## 2. Does the shape of a spherical mirror affect the amount of light it reflects?

Yes, the shape of a spherical mirror can affect the amount of light it reflects. Mirrors with a parabolic shape are known to reflect more light than those with a spherical shape.

## 3. What is the formula for calculating the area of a spherical mirror?

The formula for calculating the area of a spherical mirror is A = 4πr^2, where A is the surface area and r is the radius of the mirror.

## 4. Can the amount of light reflected by a spherical mirror be increased?

Yes, the amount of light reflected by a spherical mirror can be increased by increasing its surface area or by using a mirror with a more reflective coating, such as silver or aluminum.

## 5. How does the distance between an object and a spherical mirror affect the amount of light reflected?

The distance between an object and a spherical mirror does not directly affect the amount of light reflected. However, the position and size of the image produced by the mirror may change with varying distances, which can indirectly impact the perceived amount of reflected light.

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