Question

LIGO

is essentially a Michelson interferometer that uses

a laser light with a wavelength of

1064 nm.

The beams are initially set for destructive interference.

If the laser intensity is

200W, and

if the distances that it measure are of the order

of

10^−18m,

what will be the

intensity

of light at the detector

when it has a displacement

of this size relative to the initial (nulled)alignment)?

Answer 1

The condition for destructive interference is

Here, m is an integer m=0,+1, -1,+2,-2......

For the central minima we can take m=0 so the corresponding d becomes

The expression for the outcome intensity for destructive interference is

For destructive cos theta=-1 and ideally for destructive interference the intensity should be zero. But due to some imperfections it is not zero. Here, we are using that the resultant intensity is given as power per unit area

Here, P is the power and r is the distance, We are choosing r1 and r2 is of the order of 10^{-18}. Putting all the values in the above , we get