An optical interferometer can detect a displacement of 0.1?, or ?50nm. At what speed would a...

An optical interferometer can detect a displacement of 0.1?, or ?50nm.

At what speed would a 3.0m stick "shrink" by 50 nm? Hint: Use the binomial approximation.

Expert Solution

Length contraction is governed by equation

L = L₀ * v (1 - v² / c2)

hence change in length delta L = L₀ - L

= L0 * [1 - v (1 - v_2 / c_2) ] ----- (1)

v (1 - v^2 / c_2) = (1 - x) /2 ( where x = v^2 / c_2, )

= (1 - x/2)

= 1 - v^2 / 2c_2

delta L = L_0 * [ 1 - 1 + v^2 / 2 * c_ 2 ]

50 * 10-9m = 3.0 * v^2 / 2 * c_2

v^2 = 50 * 10-9 * 2 * c² / 3.0

= sqrt (3.33 * 10-8 ) * c²

v = 1.83 * 10-4 m/s * 3.00 * 10⁸ m/s

= 5.49 * 10⁴ m/s

genius_generous answered 3 weeks ago

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