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A question

  1. May 14, 2006 #1
    At what mass does an object start to noticeably bend light?
  2. jcsd
  3. May 14, 2006 #2


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    The angle through which light is deflected by a massive object depends on both the mass of the object, and how close the light gets to the object.

    For small angles, the formula is

    [tex]\Theta = \frac{4GM}{bc^2}[/tex]

    b is the impact parameter. This can be determined by the "distance" (really, the Schwarzschild r coordinate) at closest approach by the formula

    b = \frac{r}{\sqrt{1-\frac{2GM}{rc^2}}}

    These formulas were taken from MTW, pg 672-4, with the units converted back to standard units from "geometric" units.

    Those are the detailed formulas - you'll need to define "noticable" for us to give you a numerical answer.
  4. May 14, 2006 #3

    Hmph, fair enough. I suspected it was a vague question. Sorry about that.
  5. May 14, 2006 #4


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    If you have some specific example in mind, we can caluclate the deflection, but we need the parameters (mass, and distance of closest approach).

    I forgot to mention that the deflection by the above formula will be given in radians.

    You can see by looking at the formulae that deflection will be proportional to mass, and for large r (much greater than the Schwarzschild radius) the deflection will be inversely proportional to the distance of closest approach.
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