Question

Greenlight has a wavelength of 500 nm in air.
$\text{(i)}$ Assume green light reflected from a mirror with the angle of incidence $0^{\circ }$. The incident and reflected waves together constitute a standing wave with what distance from one node to the next node?
$\text{(ii)}$ The green light sent into a Michelson interferometer that is adjusted to produce a central bright circle. How far must the interferometer's moving mirror be shifted to change the center of the pattern into a dark circle?
Choose from the same possibilities as in part (i).
$\text{(iii)}$ The green light is reflected perpendicularly from a thin film of plastic with an index of refraction 2.00. The film appears bright in the reflected light. How much additional thickness would make the film appear dark?

• A. 1000nm
• B. 500nm
• C. 250nm
• D. 125nm
• E. 62.5nm

Answer 1

Answer: (C), (D), (E)

62.5nm
125nm
250nm

(c). The distance between nodes is half a wavelength.

(d) The reflected lights travel through the same path twice because it reflects, so moving the mirror one-quarter wavelength, 125nm, reflected in a path change of one=half wavelength, 250nm, which results in destructive interference.

(e) The wavelength of the light in the film is 500 nm/2 = 250 nm. If the film is made 62.5 nm thicker (one-quarter wavelength in the film), the light reflecting inside the film has a path length 125nm greater. This is half a wavelength, which reverses constructive into destructive interference.