Irradiance: difference between distance and the square of the distance?

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SUMMARY

The discussion centers on the relationship between distance and the square of the distance in the context of irradiance, specifically referencing the inverse square law. Participants clarify that while distance measures the space between two points, the square of the distance is a mathematical construct that does not represent a physical distance. The inverse square law states that as the distance from a point light source increases, the irradiance decreases proportionally to the square of that distance, which is mathematically expressed as 1/d².

PREREQUISITES
  • Understanding of the inverse square law in physics
  • Basic knowledge of irradiance and illuminance
  • Familiarity with mathematical concepts of squaring numbers
  • Awareness of experimental setups in physics, particularly light measurement
NEXT STEPS
  • Research the mathematical derivation of the inverse square law
  • Explore the concept of irradiance and its applications in real-world scenarios
  • Learn about experimental methods for measuring light intensity and irradiance
  • Investigate the effects of distance on light from various types of sources, including point and extended sources
USEFUL FOR

Physics students, educators, and professionals in optics or lighting design who seek to deepen their understanding of light behavior and measurement principles.

otterandseal1
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What's the difference between distance and the square of the distance?
Many Thanks
 
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otterandseal1 said:
What's the difference between distance and the square of the distance?
uhh...one is squared?

You'll need to elaborate considerably about your question if we are going to be able to help you!
 
otterandseal1 said:
What's the difference between distance and the square of the distance?
Many Thanks
The square of the distance is bigger. :smile:

I think you need to be more specific with your question. What is it you are trying to figure out?

EDIT: Ah, I see russ beat me to it
 
phinds said:
The square of the distance is bigger. :smile:

I think you need to be more specific with your question. What is it you are trying to figure out?

EDIT: Ah, I see russ beat me to it
Its to do with irradiance, I see textbooks saying "distance increases will result in irradiance decreasing" and "irradiance is inversely proportional to the square of the distance" What is the distance between the two? Sorry if I was too vague.
 
russ_watters said:
uhh...one is squared?

You'll need to elaborate considerably about your question if we are going to be able to help you!
Its to do with irradiance, I see textbooks saying "distance increases will result in irradiance decreasing" and "irradiance is inversely proportional to the square of the distance" What is the distance between the two? Sorry if I was too vague.
 
phinds said:
The square of the distance is bigger. :smile:
Unless the distance is < 1. :oldwink:
 
otterandseal1 said:
Its to do with irradiance, I see textbooks saying "distance increases will result in irradiance decreasing" and "irradiance is inversely proportional to the square of the distance" What is the distance between the two? Sorry if I was too vague.
The distance in question is the distance between the source of light and what is receiving it.

...I'm still not sure that is what you are asking though...
 
russ_watters said:
The distance in question is the distance between the source of light and what is receiving it.

...I'm still not sure that is what you are asking though...
Yes, but sometimes it refers to the distance between a source of light and then generally the square of the distance. Are they the same things? If it's more helpful, the inverse square law is the square of the distance is inversely proportional to irradiance/illuminance. What does the square of the distance mean?
 
otterandseal1 said:
Yes, but sometimes it refers to the distance between a source of light and then generally the square of the distance. Are they the same things?
"distance" is how far apart 2 points in space are. The Earth is about 150 million km from the sun, for example.
If it's more helpful, the inverse square law is the square of the distance is inversely proportional to irradiance/illuminance. What does the square of the distance mean?
Squaring something is just squaring it. 150 million km squared is 2.25 x 1016 km2.

Maybe you are asking what physical meaning this new number has? It has none, it's just a partial piece of an equation. It is not itself a distance. Notice that it no longer has units of distance...but note what units it has?!
 
  • #10
russ_watters said:
"distance" is how far apart 2 points in space are. The Earth is about 150 million km from the sun, for example.

Squaring something is just squaring it. 150 million km squared is 2.25 x 1016 km2.

Maybe you are asking what physical meaning this new number has? It has none, it's just a partial piece of an equation. It is not itself a distance. Notice that it no longer has units of distance...but note what units it has?!
Is the symbol 1/d^2 the square of a distance then?
So if I said as the distance from a point source increases, the irradiance decreases, would this be an effective conclusion of the inverse square law?
 
  • #11
otterandseal1 said:
Is the symbol 1/d^2 the square of a distance then?
So if I said as the distance from a point source increases, the irradiance decreases, would this be an effective conclusion of the inverse square law?
Near enough when the source can be regarded as a point source. An extended source like big nebulae or galaxies *Sun and Moon, too) need some adjustment.
Go into the garden at night and see the effect of the light from a picture window as you walk away, trying to read a book. Definitely not ISL.
 
  • #12
otterandseal1 said:
Is the symbol 1/d^2 the square of a distance then?
So if I said as the distance from a point source increases, the irradiance decreases, would this be an effective conclusion of the inverse square law?
Yes. The irradiance decreases faster with a square in the equation than without. That's it.
 
  • #13
russ_watters said:
Yes. The irradiance decreases faster with a square in the equation than without. That's it.
Sorry just to double check 1/d^2 is not the same as the square of the distance is it?
 
  • #14
otterandseal1 said:
Sorry just to double check 1/d^2 is not the same as the square of the distance is it?
No, it's 1 divided by the square of the distance.
 
  • #15
russ_watters said:
No, it's 1 divided by the square of the distance.
In irradiance experiments, why is a black sheet placed underneath the light meter and the light bulb?
 
  • #16
otterandseal1 said:
In irradiance experiments, why is a black sheet placed underneath the light meter and the light bulb?
Probably to cut down on reflected light to make the experimental results better fit the inverse square law.
 
  • #17
jtbell said:
Unless the distance is < 1. :oldwink:
Hey, watch it! Nitpicking here is MY job :smile:
 

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