A mad scientist wishes to put a giant lens into orbit to focus the sun’s rays in

Question

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 × 107 m above the earth). The sun is 1.5 × 1011 m from the earth and puts out about 4 × 1026 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 × 105 m2 . Can the mad scientist produce this level of intensity? If so, how, and if not, why not?

Explanation / Answer

apply focal length f = R/2 = 1.5 e 11/2 = 7.5 e 10 m

so now use lens maker equation as

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

here R2 = infinity for flat surface

so

1/ 7.5 e 10 = (1.5-1) *(1/R2 - 0)

1/R2 = 2/7.5 e 10

R2 = 3.75 e 10 m

this must be a diverging lens so that image falls on retina

-----------------------------------------

b. intensity I = power/area

I = 4 e26/(4pi * 3.58 e7 *3.58 e7)

I = 9.9 e 10 W/m^2 is the the actual intensity

so

with laser

Intensity I = P/A

1 trillion = 10^12

I = 500 * 10^12 /2.5 e-5

I = 2.024 e10 W/m^2

so no scientist cannot produce intensity of that level

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