Optics - Michelson Interferometer

A Michelson interferometer is configured as a wave-meter, as shown in the figure above, so that a ratio of fringe counts may be used to compare the wavelength of two lasers with high precision. When the mirror in the right arm of the interferometer is translated through a distance d, 100,000 interference fringes pass across the detector for green light and 85,865 fringes pass across the detector for red (λ = 632.82 nanometers) light. The wavelength of the green laser light is

A. 500.33 nm

B. 543.37 nm

C. 590.19 nm

D. 736.99 nm

E. 858.65 nm

(GR0177 #100)

Solution

λ_red = 632.82 nm

λ_red  λ_green → (D) and (E) are FALSE.

Constructive path difference = Nλ

N_gλ_g = N_rλ_r

λ_g = N_rλ_r / N_g

= (85,865 × 632.82) / 100,000

≈ (8.6 × 10⁴ × 6.3 × 10²) / 10⁵

= 541.8

Answer: B