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

otterandseal1
What's the difference between distance and the square of the distance?
Many Thanks

Mentor
What's the difference between distance and the square of the distance?
uhh...one is squared?

Gold Member
2022 Award
What's the difference between distance and the square of the distance?
Many Thanks
The square of the distance is bigger. 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

otterandseal1
The square of the distance is bigger. 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.

otterandseal1
uhh...one is squared?

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.

Mentor
The square of the distance is bigger. Unless the distance is < 1. Mentor
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...

otterandseal1
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?

Mentor
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?!

otterandseal1
"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?

Gold Member
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.

Mentor
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.

otterandseal1
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?

Mentor
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.

otterandseal1
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?

Mentor
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.

Unless the distance is < 1. Hey, watch it! Nitpicking here is MY job 