Inverse Square Law: Magnifying Glass & Sunlight

In summary, the inverse square law does not play a significant role in the burning of a piece of paper with a magnifying glass on a sunny day. The focal length of the lens has more to do with sharp focus than the amount of light on the film. The inverse square law is a manifestation of spherical symmetry and does not apply to all light sources. The size and temperature of the hot spot, as well as the type of light source, also affect the burning process. The ISL only applies when the source is small enough to be considered a point source.
  • #1
thared33
2
0
I found this forum on Google. This may not be the right section so excuse me if so. I have a rather simple question though.

When you take a magnifying glass on a sunny day and position it just right over a piece of paper, the paper will start to burn. Is the inverse square law (distance) the biggest factor at play in getting the paper to burn? Or is it more that due to the way the lens is positioned, it concentrates the light into a single point rather than diffuse it?
 
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  • #2
thared33 said:
When you take a magnifying glass on a sunny day and position it just right over a piece of paper, the paper will start to burn. Is the inverse square law (distance) the biggest factor at play in getting the paper to burn?
No.
Or is it more that due to the way the lens is positioned, it concentrates the light into a single point rather than diffuse it?
Yes.

The simple form of the inverse square law describes what happens to light propagating freely away from its source and dispersing as it goes. When you add a lens into the picture, it no longer applies.
 
  • #3
On a camera, the focal length of a lens (how close/far the lens is from the film) has something to do with the amount of light that hits the frame of film. Is that because of the inverse square law?
 
  • #4
thared33 said:
On a camera, the focal length of a lens (how close/far the lens is from the film) has something to do with the amount of light that hits the frame of film. Is that because of the inverse square law?

No. The inverse square law is about how energy spreads out from an energy source. The focal length of a lens has more to do with sharp focus than with the amount of light on the film. It tells how far the film should be from the lens for the light from a single point of the object being photographed to be focused on a single point of the film.
 
  • #5
The inverse square law is a manifestation of spherical symmetry.
 
  • #6
Burning or not will depend on several factors. The area of the lens will determine how much solar radiation is captured (based on 1kW per meter squared - which is determined by the ISL but is the same for all lenses in clear sunlight).
The temperature of the hot spot will depend on its size (the optics) and the rate at which heat is conducted away from the spot. A thin piece of paper, protected from drafts will burn easier than a fat piece of cardboard (or metal).
 
  • #7
Adding to what others have said, the inverse square law would have a role to play if you were trying to burn the paper using e.g., a naked lighbulb. Since we can approximately treat the bulb as a point source radiating in all directions, the farther you get from it the less energy you catch.

When treated as one, a lens is a completely different kind of source. It most definitely does not radiate equally in all directions, so inverse square law does not apply.

There are other kinds of light sources that do not obey the inverse square relationship. Think of a prefectly collimated laser beam - no matter how far you get from the source, you get the same amount of energy per area.


In principle, the inverse square law does play a role when trying to burn something with a lens in the sense that as you position the lens closer to the Sun, it catches a bit more of its energy than if you put farther away(i.e., closer to the ground). That's because the Sun does radiate (approximatelly)equally in all directions, so the amount of incident energy does fall as a square of the distance.
Of course, since the change of distance of a few centimetres, or even thousands of kilometres, is so minuscle as compared to the distance from the Sun, the difference in received light is absolutely and completely negligible(so it's perfectly safe to assume the energy received from the Sun on Earth is independent of distance, and all light rays coming from it are parallel).
 
  • #8
All else being equal (equal sized lens, equal distance from light source, equal distance from lens to film.), the focal length of the lens does not change the amount of light that hits the film as long as the film is large enough to catch all the light and nothing else blocks it. Focal length only changes how the light is focused.
 
  • #9
Bandersnatch said:
When treated as one, a lens is a completely different kind of source. It most definitely does not radiate equally in all directions, so inverse square law does not apply.

This is not actually true. A source does not need to be isotropic for the ISL to apply. The power flux in a given direction does not affect the flux in another direction. All that is necessary is for the source to be small enough to regard as a point source. An extended source will exhibit the ISL once you get far enough away to regard it as a point source. (i.e. subtends a 'sufficiently' small angle).
 
  • #10
Huh. Thanks sophiecentaur, I see now how one does not necessarily follow from the other.
 

1. What is the Inverse Square Law and how does it relate to magnifying glasses and sunlight?

The Inverse Square Law is a physical principle that describes the relationship between the intensity of radiation (such as light) and the distance from its source. It states that the intensity of radiation decreases in proportion to the square of the distance from the source. In the case of magnifying glasses and sunlight, this means that the closer the lens of the magnifying glass is to the sun, the more concentrated and intense the sunlight will be.

2. How does the Inverse Square Law affect the size of the focal point created by a magnifying glass?

The Inverse Square Law also applies to the size of the focal point created by a magnifying glass. As the distance between the lens and the focal point decreases, the focal point becomes smaller and more intense. This is why moving the magnifying glass closer to the object being magnified will result in a smaller and more concentrated focal point.

3. Can the Inverse Square Law be used to explain why magnifying glasses can start fires?

Yes, the Inverse Square Law can explain why magnifying glasses can start fires. When the lens of a magnifying glass is held at the correct distance from the object and the sun, the sunlight is concentrated and intensified at the focal point. This intense heat is enough to ignite a fire.

4. How does the Inverse Square Law affect the intensity of light from the sun at different distances from the Earth?

The Inverse Square Law applies to the intensity of light from the sun at different distances from the Earth. This means that the further away from the sun an object is, the less intense the sunlight will be. For example, at twice the distance from the sun, the intensity of sunlight will be reduced to one-quarter of its original value.

5. What are some practical applications of the Inverse Square Law in everyday life?

The Inverse Square Law has many practical applications in everyday life. For example, it is used in photography to control the amount of light hitting the camera's sensor. It is also used in radiation therapy to determine the safe distance from patients to the radiation source. In addition, the Inverse Square Law is used in astronomy to measure the brightness of stars and in satellite communication to calculate the strength of signals from space.

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