Apparent magnitude of a light bulb

[icedragon]

Homework Statement

What is the apparent magnitude of a 100W light bulb at a distance of 3 m?

[Hint: Compare with the Sun to eliminate the unknown constant in the expression relating flux density to apparent magnitude.]

. The solar luminosity is $L \approx 4 \times 10^{26} W$.
. The Earth-Sun distance is approximately $1.5 \times 10^8 km$.

Homework Equations

$m-M=5log \frac{d}{10}$
$m=-2.5log \frac{l}{l_{0}}$

The Attempt at a Solution

I have attempted to substitute m into the equation for m-M but I do not see how that helps me eliminate the unknown constant (which I assume is $l_{0}$. Any help would be appreciated!

 

[collinsmark]

Hello icedragon,

Welcome to Physics Forums (PF)!

Homework Statement

What is the apparent magnitude of a 100W light bulb at a distance of 3 m?

[Hint: Compare with the Sun to eliminate the unknown constant in the expression relating flux density to apparent magnitude.]

. The solar luminosity is $L \approx 4 \times 10^{26} W$.
. The Earth-Sun distance is approximately $1.5 \times 10^8 km$.

Homework Equations

$m-M=5log \frac{d}{10}$

Where did that formula come from? What's d and where did the '10' come from?

$m=-2.5log \frac{l}{l_{0}}$

(In your equation you are using $l$'s as in 'lesson'. But they should be capitol $I$'s as in 'Intensity'.)

That looks right if the relative magnitude of $I_0$ is 0 (which is just fine for what we're doing in this problem).

The more general formula is

$$m_1 - m_0 = -2.5 \log \frac{I_1}{I_0}$$
which you can then set $m_0 = 0$ if you want $m_1$ to be relative to 0 magnitude. But you'll still need to solve for $I_0$ if you wish to do that.

The Attempt at a Solution

I have attempted to substitute m into the equation for m-M but I do not see how that helps me eliminate the unknown constant (which I assume is $l_{0}$. Any help would be appreciated!

If it helps, the relative magnitude of the sun is -27 (relative to magnitude 0)*. Your first step is to use that and solve for $I_0$.

*(See http://en.wikipedia.org/wiki/Magnitude_%28astronomy%29)