Calculating Angular Spread of Light in Glass Using Snell's Law

[skinard360]

Homework Statement

A sheet of glass has n_red=1.52 and n_violet=1.55. A narrow beam of white light is incident on the glass at 27.0 degrees
What is the angular spread of the light inside the glass?

Homework Equations

Snells Law: theta2 = arc sin (n1 sin theta1)/n2

The Attempt at a Solution

I tried two ways of answering this question and neither has worked. First I made two equations: n1=red(1.51), theta1=27, n2=air(1.00)...then a second equation with n1=violet(1.55)...then subtracted the two thetas

My second attmept was to set n1=glass(1.5)...all else the same as above
Neither attempt was correct, can someone please help??

 

[Mentz114]

Make two simple calculations, one for theta red, and one for theta blue, then subtract them. You must have made an arithmetic error. Are you using degrees or radians in your calculator ?

 

[skinard360]

I tried it in degrees and got .014 but it was wrong :(

 

[hage567]

Are you dividing by n2 before taking the arcsin? (you should be)

 

[skinard360]

i wasn't doing that, but once I tried it my answer was still wrong...here is exactly what I'm doing:

[arcsin (1.55 sin 27)/1.5] - [arcsin (1.52 sin 27)/1.5] = .587 degrees

 

[hage567]

I think I see what you are doing wrong.

This is the equation you had, and it's correct:

theta2 = arc sin (n1 sin theta1)/n2

but n1 is the index of refraction of AIR, since the light is incident on the glass (i.e. going from air into the glass). You are trying to find the angle of refraction. n2 should be either 1.55 or 1.52, depending on which wavelength you are considering. You have it flipped around in your calculation.

I don't understand why you would make n2=1.5

 

[skinard360]

you are right! thank you :)