What formula to use?

Question

A certain kind of glass has an index of refraction of 1.650 for blue light of wavelength 430 nm. and an index of 1.615 for red light of wavelenth 680nm. IF a beam containing these two colors is incident at an angle of 30 deg. on a piece of this glass, what is the angle between the two beams inside the glass?

Answer 1

The pertinent formula to use would be Snell’s Law,
n1 * sin (theta_1) = n2 * sin (theta_2)
Where n1 and n2 are the indices of refraction for the initial and final medium for particular wavelength of light and theta_1 and theta_2 are the incident and refracted angles of the light with respect to the normal.

You will want to solve the above formula for theta_2,
Theta_2 = arcsin (n1 * sin (theta_1) / n2) = sin^-1 (n1 * sin (theta_1) / n2)
You are given a value for n1, theta_1, and n2 in the question, so you should not be able to find the refracted angles for each of the wavelengths.

All you need do now, after finding the refracted angles of the light, is to find the difference between them.


*By the way, good for you just asking for the formula to use and not the entire worked out solution.
The important thing to gain here is to recognize that one can manipulate Snell’s law around to solve for different, unknown, variables when you know everything else. After you recognize that you can solve for theta_2 in terms of n1, n2, and theta_2, everything else is trivial.

Answer 2

Haven't done physics for a while, but give Snell's law a shot... here's a link i found to the equation. Maybe there is something else on here that can help.

Answer 3

use snells law: n1sin(theta1) = n2sin(theta2)

since in air n = ~1

sin (30) = n2 sin(theta2)

or

sin (30) / n2 = sin (theta2)

take sin-1 of both sides and you have theta2... do this for both colors and find the difference, that's your angle between the two colors.