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Apparent magnitude of a light bulb

  1. Nov 14, 2012 #1
    1. The problem statement, all variables and given/known data

    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 [itex]L \approx 4 \times 10^{26} W[/itex].
    . The Earth-Sun distance is approximately [itex]1.5 \times 10^8 km[/itex].

    2. Relevant equations

    [itex]m-M=5log \frac{d}{10}[/itex]
    [itex]m=-2.5log \frac{l}{l_{0}}[/itex]

    3. 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 [itex]l_{0}[/itex]. Any help would be appreciated!
     
    Last edited: Nov 14, 2012
  2. jcsd
  3. Nov 14, 2012 #2

    collinsmark

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    Hello icedragon,

    Welcome to Physics Forums (PF)!
    Where did that formula come from? What's d and where did the '10' come from?
    (In your equation you are using [itex] l [/itex]'s as in 'lesson'. But they should be capitol [itex] I [/itex]'s as in 'Intensity'.)

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

    The more general formula is

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

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