Nuclear-pumped x-ray lasers are seen as a possible weapon to destroy ICBM booste
ID: 1380186 • Letter: N
Question
Nuclear-pumped x-ray lasers are seen as a possible weapon to destroy ICBM booster rockets at ranges up to 2000 km. One limitation on such a device is the spreading of the beam due to diffraction, with resulting dilution of beam intensity. Consider such a laser operating at a wavelength of 1.00 nm. The element that emits light is the end of a wire with diameter 0.210 mm. (a) Calculate the diameter of the central beam at a target 2000 km away from the beam source. (b) By what factor is the beam intensity reduced in transit to the target? (The laser is fired from space, so that atmospheric absorption can be ignored.)
Explanation / Answer
sin theta = 1.22 lamda/d = 1.22*(1.0 x 10-9m)/(0.210 x 10-3m) = 5.81E-06
theta is the same (in radians)
0.210 x 10^-3*= 5.81E-06*2000000m = 2.44 mm diameter after all of this way.
Intensity goes as area, which goes as diameter squared. Ratio of the two diameters squared is
(.210 mm/2.44 mm)^2 = 0.0074
So the intensity is 0.74% as much as it was
It is reduced by a factor of 1/.0074 = 135
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