Final answer:
To determine the index of refraction n of a thin film, the equation is rearranged to n = (mλ)/(2t), where m is the interference order, λ is the light's wavelength, and t is the film's thickness.
Step-by-step explanation:
To rearrange the equation 2t = (mλ)/n to determine the index of refraction n of a thin film, one must isolate n on one side of the equation. This results in the formula n = (mλ)/(2t), where m is the order of the interference (an integer), λ is the wavelength of the incident light in vacuum, and t is the thickness of the film.
To minimize the reflection of normally incident light from a thin film, the thickness t should be such that the path length difference between the two rays that interfere is a half-integral multiple of the wavelength in the medium. If we assume the light undergoes a half-wavelength phase shift upon reflection at the boundary with a higher index of refraction, the condition for destructive interference (and thus minimized reflection) is achieved when λ is an odd multiple of λ/(4n), meaning that t should equal (2m + 1)λ/(4n) for some integer m.