Red and Violet Light through a Prism (Snell's Law)

[Venerable R]

Homework Statement

A ray of white light strikes the surface of a 4.0-cm-thick slab of flint glass (Θ1 = 60°). As the ray enters the glass, it is dispersed into its constituent colors.

Estimate how far apart the rays of deepest red and deepest violet light are as they exit the bottom surface. Assume nred = 1.57 and nviolet = 1.60.

Θ1 = 60°
n1 = 1 (air)
Θ2violet = ?
Θ2red = ?
nviolet = 1.60
nred =1.57
d (adj) = 4 cm
Δx = ?

Homework Equations

Snell's Law: n1*sin(Θ1) = n2*sin(Θ2)
tan(Θ) = opp/adj

The Attempt at a Solution

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n1*sin(Θ1) = n2*sin(Θ2r)
sin^-1((sin 60°)/(1.57)) = Θ2r = 33.5°

n1*sin(Θ1) = n2*sin(Θ2v)
sin^-1((sin 60°)/(1.60)) = Θ2v = 32.8°

tan(Θ2r) = opp/adj
dr = tan(33.5°) * 4 cm = 2.65 cm

dv = tan(32.8°) * 4 cm = 2.58 cm

Δx = 2.65 cm - 2.58 cm = 0.7 mm

It says that this answer is not correct, but I am nearly 100% sure this is how it should be done!

 

[TSny]

Your work looks correct to me. Since no picture is provided, it is important to know how the angle of 60^o is measured. I assume it's the angle between the incoming light ray and the normal to the surface of the glass.

 

[Venerable R]

Your work looks correct to me. Since no picture is provided, it is important to know how the angle of 60^o is measured. I assume it's the angle between the incoming light ray and the normal to the surface of the glass.

Yeah, I'm really unsure of why it's marking me wrong. Here's the reference figure: http://i.imgur.com/5r2P1vY.jpg?1

 

[TSny]

Ah. Note that the 60^o shown in the figure is not the angle of incidence.

 

[Venerable R]

Ah. Note that the 60^o shown in the figure is not the angle of incidence.

Ah! Thank you so much! The correct answer came out to be 0.28 mm.

 

[abbas_majidi]

Hi
For finding separation distance you must multiply your answer by sin(60). This is shown in below link:

https://www.dropbox.com/s/zpbmoy5zwm1lzu6/IMG_20150328_235418.jpg?dl=0

 

[TSny]

Hi
For finding separation distance you must multiply your answer by sin(60). This is shown in below link:

https://www.dropbox.com/s/zpbmoy5zwm1lzu6/IMG_20150328_235418.jpg?dl=0

Yes, good point. The usual interpretation of "How far apart are two parallel rays?" would be as you have shown.