Light passing from one medium to another is refracted because the speed of light is different in the two media. It is generally found that the speed of light in any material is less than the speed of light in vacuum. Light travels at its maximum speed in vacuum.
The index of refraction for a medium is conveniently defined as n equal to
(speed of light in vacuum) / (speed of light in a medium) or (c ÷ v). The index of refraction is a dimensionless number greater than unity since v is always less than c. Furthermore, n is equal to unity in vacuum.
As light travels from one medium to another, the frequency of the light does not change. Consider wavefronts passing Mike in Medium 1 with a certain frequency and incident in the boundary between Medium 1 and Medium 2. The frequency with which the wavefronts pass Kim in Medium 2 must equal the frequency at which they reach Mike in Medium 1. Otherwise, either wavefronts would be piling up at the medium boundary or they would be destroyed or created at the boundary. There is no mechanism to cause such "piling", destruction, or creation so the frequency must be a constant as a light ray passes from one medium into another.
It then follows that, because the relation v = fλ must be valid in both media and because f1 = f2 = f, one sees that v1 = fλ1 and v2 = fλ2. A relationship between index of refraction and wavelength is obtained by:
f = (v1/λ1) = (v2/λ2) or (λ1/λ2) is
(v1/v2) equal to (c/n1) ÷ (c/n2) which amounts to (n2/n1). Then λ1n1 = λ2n2.
If Medium 1 is a vacuum (or, for all practical purposes, air), then n1 = 1. Thus,
(λ1/λ2) = (n2/n1) or (λ1/λ2) = (n2/1).
For the problem posed, n2 = n and n1 = 1, so (λ1/λ2) equals (n/1) or n:1, which is Choice C for the multiple choices given.
