Question

In the 1887 experiment by Michelson and Morley, the length of each arm was 11 m. The experimental limit for the fringe shift was 0.005 fringes. If sodium light was used with the interferometer (λ = 589 nm), what upper limit did the null experiment place on the speed of the Earth through the expected ether?

Answer 1

v = 3470 m/s

Explanation:

given data:

suppose n be the number of fringes shifted which is equal to 0.005

wavelength of light is given as 589 nm

difference light path is given as
`\lambda n = \Delta d`

but we know that

`\Delta d = c(\Delta t' -\Delta t)`

`(\Delta t' -\Delta t) =(v^2(l1+l2))/(c^3)`

but in the question we have given that

l1=l2 = 11 m

therefore we have

`\lambda n = c(v^2(2l))/(c^3)`

solving for v, we get

`v = c\sqrt {(\lambda n)/(2l)}`

`v = 3*10^8\sqrt {(589*10^(-9)*0.005)/(2*11)}`

v = 3470 m/s