4) A mad scientist wishes to put a giant lens into orbit to focus the sun\'s ray

Question

4) A mad scientist wishes to put a giant lens into orbit to focus the sun's rays into a death beam. He plans to launch it to a geosynchronous orbit (about 3.58 x 10^7 m above the earth). The sun is 1.5 x 10^11 m from the earth and puts out about 4 x 10^26 W of power. (a) Suppose one side of the lens must be flat. About what radius of curvature must the other side be (be sure to note whether the lens should be converging or diverging and why)? Assume he uses glass with n = 1.5. (b) The most intense man - made beam ever produced is probably at the National Ignition Facility at Lawrence Livermore National Laboratory. They have made a 500 trillion Watt laser intended to focus on a target of roughly 2.5 x 10^ - 5 m^2. Can the mad scientist produce this level of intensity if he wants his beam to cover an area of .25 m^2? If so, how, and if not, why not?

Explanation / Answer

the lens makers formula for plano convex lens is

1/f = ( n-1) ( 1/R1 +1/ R2)

2/R = ( 1.5-1) ( 1/ infinity + 1/ R2)

    2/R= 0.5 ( 1/ R2)

R =4 R2

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intensity of laser beam is

I = P/A = 500* 10 ^12 W/2.5 * 10 ^-5 m^2 = 200 * 10 ^7 W/m^2

the intensity of sunrays

I = P/A = 4 * 10^26 W/ 0.25 m^2 = 16 * 10 ^26 W/m^2

from the above two intesnities the mad sceintis procue the intensity of laser light

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