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Chapter2_19

Chapter2_19 - W c R GM c gW W gt W d 2 2 2 2 2 2 2 = = =...

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PHY3063 R. D. Field Department of Physics Chapter2_19.doc University of Florida The Deflection of Light by Gravity The equivalence principle predicts that light is deflected by a gravitational field. Frame 1 (at rest, gravity): Consider a light ray traveling through a hole in a box of width W. The hold is located a height h above the floor and the box is at rest in a gravitational field with gravitational acceleration g = GM/R 2 . Frame 2 (accelerated, no gravity): Suppose that the light entered the box at t = 0. It takes the light a time t = W/c to cross the box. At time t the detector has speed v = gt and has moved upward a distance d = gt 2 /2. In frame 2 the angular deflection of the light is The radiation travels at speed c and thus
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Unformatted text preview: W c R GM c gW W gt W d 2 2 2 2 2 2 2 = = = ≈ θ . Frame 1 (at rest, gravity): The same thing must occur in both frame 1 and frame 2 so in frame 2 this would be interpreted as the light “falling” in the gravitational field ( i.e. being pulled toward the large mass). Deflection of Light in a Gravitational Field: 2 2 c r GM ≈ Large Mass M R Inertial frame in a gravity field Light Ray Frame 1 h h W Accelerated frame (no gravity) Light Ray Frame 2 (t = 0) h h W a = g Accelerated frame (no gravity) Light Ray Frame 2 (t = W/c) d = gt 2 /2 h W a = g θ Large Mass M R Light bent by gravity Light Ray Frame 1 h W θ Light Path Large Mass M R Light bent by gravity Light Ray θ r Distance of closest approach!...
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