<p>You can easily convert flux to luminosity and vice versa using the spherical nature of the propagation of light. The equation you need is:</p>

<p>$$
L=4\pi D^{2}f
$$
Where $f$ will be your flux, and $D$ is the distance to the object, Tau Ceti in this case.</p>

<p>From Pijpers (2003) Tau Ceti's luminosity is $0.52\pm0.03L_{\odot}$. You should have everything you need there. $L_{\odot}$ is of course the luminosity of the Sun. </p>

CC BY-SA 3.0
2015-12-02T21:30:58.967Z
I don't quite understand (I'm not that good at Physics). I'm looking to convert to illuminance (measured in lux). Is this the same as flux?
Shuri2060
CC BY-SA 3.0
2015-12-02T21:46:22.403Z
Illuminance is the total luminous flux incident on a surface, per unit area. So $I=f/A$, so what is your area, $A$, of your surface? (then you can re-arrange my equation for to obtain the luminosity)...
MichaelJRoberts
CC BY-SA 3.0
2015-12-02T22:40:32.990Z
I still don't quite understand and don't see how area is involved in this..... The original experiment involved me using a light meter and a light bulb with the distance increasing between them at each reading. The light meter read in lux, and I derived an inverse relationship..... But no area involved. I am told by Wikipedia that the illuminance of the Sun is around 120,000 lux at its brightest. Now, knowing also the distance to the Sun, I expected that if the illuminance of Tau Ceti was known, I could just use these 3 values to find the distance to Tau Ceti.
Shuri2060
CC BY-SA 3.0
2015-12-02T22:41:21.263Z
But I can't see how area is involved in this
Shuri2060
CC BY-SA 3.0
2015-12-02T22:45:05.557Z
So illuminance is defined as the flux per unit area. Your measuring device will have a light capturing device which has a well defined area, maybe a few square inches. So, you get your illuminance. If you convert to a flux by knowing the capture area of your device you can then use all the known variables and the equations given to start calculating distances. Maybe you can't use the method you have prescribed?
MichaelJRoberts
CC BY-SA 3.0
2015-12-02T22:46:30.847Z
And it would be very hard to measure the illuminance of one solitary star. Think about what other sources of light would hit an illuminance detector. Hence why flux is often used.
MichaelJRoberts
CC BY-SA 3.0
2015-12-02T22:50:41.860Z
But you could take the luminosity I have given for Tau Ceti, find the light capture area of your device, then convert the illuminance you measured for the Sun into a flux then into luminosity and use a similar inverse relationship to derive the distance to Tau Ceti.
MichaelJRoberts
CC BY-SA 3.0
2015-12-02T12:56:53.517Z
2015-12-02T12:56:53.517Z
MichaelJRoberts
<p>As part of my physics project, I investigated the relationship between a light bulb's illuminance and the distance from the measuring device to it.</p>

<p>Illuminance was measured in flux, and distance in metres.</p>

<p>I derived an inverse relationship. First of all, can I check if this is the relationship I was supposed to get? (I understand that there is an inverse square relationship between luminosity and distance, but since illuminance is measured in lumens/sq metre, then I think an inverse relationship is correct...)</p>

<p>Next, using this relationship, I need to extend my project so that I can find distances to stars using this relationship.</p>

<p>As long as 2 stars have a similar mass/size/density, then I can use this relationship to find the distance to the 2nd star as long as the illuminance of the stars are known, and the distance to the 1st star is known.</p>

<p>So I tried to do this with an example - the Sun and Tau Ceti, as they are reasonably similar.</p>

<p>I have values for the Sun's distance/illuminance - $1.5\!\times\!10^8 $km, $1.2\!\times\!10^5$lux.
I now am trying to calculate the distance to Tau Ceti using this method.... But nowhere can I find a value for its illuminance.</p>

<p>Please can someone help me with this? Is there a way to convert from apparent magnitude or luminosity to illuminance?</p>

<p>Thank you</p>

<p>EDIT: The method I want to use from the inverse relationship is:</p>

<p>$$d_2=d_1l_1/l_2$$</p>

<p>where $d_1$ and $l_1$ are the known distance and illuminance of the 1st star, whilst $d_2$ and $l_2$ is that of the second, and $d_2$ is unknown.</p>

CC BY-SA 3.0
2015-12-02T21:31:57.153Z
I'm not looking for that, as I'm trying to convert to illuminance (measured in lux)
Shuri2060
CC BY-SA 3.0
2015-12-03T19:21:24.287Z
Thank you, but as stated above, I need to use the illuminance due to the nature of my project.
Shuri2060
<star><luminosity>
What is the illuminance of Tau Ceti?
Shuri2060
# What is the illuminance of Tau Ceti?

(Asked by: username_0 on 2015-12-02)

As part of my physics project, I investigated the relationship between a light bulb's illuminance and the distance from the measuring device to it.

Illuminance was measured in flux, and distance in metres.

I derived an inverse relationship. First of all, can I check if this is the relationship I was supposed to get? (I understand that there is an inverse square relationship between luminosity and distance, but since illuminance is measured in lumens/sq metre, then I think an inverse relationship is correct...)

Next, using this relationship, I need to extend my project so that I can find distances to stars using this relationship.

As long as 2 stars have a similar mass/size/density, then I can use this relationship to find the distance to the 2nd star as long as the illuminance of the stars are known, and the distance to the 1st star is known.

So I tried to do this with an example - the Sun and Tau Ceti, as they are reasonably similar.

I have values for the Sun's distance/illuminance - $1.5\!\times\!10^8 $km, $1.2\!\times\!10^5$lux.
I now am trying to calculate the distance to Tau Ceti using this method.... But nowhere can I find a value for its illuminance.

Please can someone help me with this? Is there a way to convert from apparent magnitude or luminosity to illuminance?

Thank you

EDIT: The method I want to use from the inverse relationship is:

$$d\_2=d\_1l\_1/l\_2$$

where $d\_1$ and $l\_1$ are the known distance and illuminance of the 1st star, whilst $d\_2$ and $l\_2$ is that of the second, and $d\_2$ is unknown.

**Tags:** star, luminosity

> **Comments:**
> **username_0**: I'm not looking for that, as I'm trying to convert to illuminance (measured in lux)  
> **username_0**: Thank you, but as stated above, I need to use the illuminance due to the nature of my project.  

---

## 1 answers

### Answer by username_1 on 2015-12-02. Score: 3

You can easily convert flux to luminosity and vice versa using the spherical nature of the propagation of light. The equation you need is:

$$
L=4\pi D^{2}f
$$
Where $f$ will be your flux, and $D$ is the distance to the object, Tau Ceti in this case.

From Pijpers (2003) Tau Ceti's luminosity is $0.52\pm0.03L\_{\odot}$. You should have everything you need there. $L\_{\odot}$ is of course the luminosity of the Sun.

> **Comments:**
> **username_0**: I don't quite understand (I'm not that good at Physics). I'm looking to convert to illuminance (measured in lux). Is this the same as flux?  
> **username_1**: Illuminance is the total luminous flux incident on a surface, per unit area. So $I=f/A$, so what is your area, $A$, of your surface? (then you can re-arrange my equation for to obtain the luminosity)...  
> **username_0**: I still don't quite understand and don't see how area is involved in this..... The original experiment involved me using a light meter and a light bulb with the distance increasing between them at each reading. The light meter read in lux, and I derived an inverse relationship..... But no area involved. I am told by Wikipedia that the illuminance of the Sun is around 120,000 lux at its brightest. Now, knowing also the distance to the Sun, I expected that if the illuminance of Tau Ceti was known, I could just use these 3 values to find the distance to Tau Ceti.  
> **username_0**: But I can't see how area is involved in this  
> **username_1**: So illuminance is defined as the flux per unit area. Your measuring device will have a light capturing device which has a well defined area, maybe a few square inches. So, you get your illuminance. If you convert to a flux by knowing the capture area of your device you can then use all the known variables and the equations given to start calculating distances. Maybe you can't use the method you have prescribed?  
> **username_1**: And it would be very hard to measure the illuminance of one solitary star. Think about what other sources of light would hit an illuminance detector. Hence why flux is often used.  
> **username_1**: But you could take the luminosity I have given for Tau Ceti, find the light capture area of your device, then convert the illuminance you measured for the Sun into a flux then into luminosity and use a similar inverse relationship to derive the distance to Tau Ceti.  

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