Question

Jan first uses a Michelson interferometer with the 606 nmnm light from a krypton-86 lamp. He displaces the movable mirror away from him, counting 818 fringes moving across a line in his field of view. Then Linda replaces the krypton lamp with filtered 502 nmnm light from a helium lamp and displaces the movable mirror toward her. She also counts 818 fringes, but they move across the line in her field of view opposite to the direction they moved for Jan. Assume that both Jan and Linda counted to 818 correctly.

a) what distance did each person move the mirror?
b) resultant displacement of the mirror

Answer 1

Answer:

a) d₁ = 247.8 μm

d₂ = 205.3 μm

b) d₂ = 20.53 x 10⁻⁵ m = 205.3 μm

Explanation:

a)

The formula for Michelson Interferometer is derived to be:

d = mλ/2

where,

d = distance moved

m = no. of fringes

λ = wavelength of light

For JAN, we have following data

d = d₁

m = 818

λ = 606 nm = 606 x 10⁻⁹ m

Therefore,

d₁ = (818)(606 x 10⁻⁹ m)/2

d₁ = 24.78 x 10⁻⁵ m = 247.8 μm

For LINDA, we have following data

d = d₂

m = 818

λ = 502 nm = 502 x 10⁻⁹ m

Therefore,

d₂ = (818)(502 x 10⁻⁹ m)/2

d₂ = 20.53 x 10⁻⁵ m = 205.3 μm

b)

The resultant displacement can be found out from the difference between both displacement. And the direction of resultant displacement will be the same as the direction of greater displacement. Therefore,

Resultant Displacement = Δd = d₁ - d₂

Δd = 247.8 μm - 205.3 μm

Δd = 42.5 μm (in the direction of JAN)