To solve this problem, we should remember that the formula
for index of refraction is defined as:
n = c / v
or
n v = c
Where,
n = index of refraction
c = speed of light
v = speed of light in the medium
Since speed of light is constant, then we can simply
equate the materials 1 and 2:
n1 v1 = n2 v2
Where the speed of light in the medium (v) can be expressed
as:
v = w * f
Where,
w = wavelength of light
f = frequency of light
Therefore substituting this back into the relating equation:
<span>n1 </span>w1 f1 = <span>n1 </span>w2 f1
Since it is given that the light is
monochromatic, w1 = w2, this further simplifies the equation to:
n1 f1 = n2 f2
<span>f1 / f2 = n2 / n1 (ANSWER)</span>