Nuclear-pumped x-ray lasers are seen as a possible weapon to destroy ICBM booste

Question

Nuclear-pumped x-ray lasers are seen as a possible weapon to destroy ICBM booster rockets at ranges up to 2250 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 0.250 mm. 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

the diameter of the central beam :

D = 1.22[lambda*L/d] = 1.22*[1x10-9*2250x103 / 0.25x10-3] = 10.98 m

ratio of the intensities:

I1/I2 = [d/D]2

= [0.25x10-3/10.98]2

= 5.184X10-10

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