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

  • #1

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


[/B]
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!
 

Answers and Replies

  • #2
TSny
Homework Helper
Gold Member
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Your work looks correct to me. Since no picture is provided, it is important to know how the angle of 60o is measured. I assume it's the angle between the incoming light ray and the normal to the surface of the glass.
 
  • #3
Your work looks correct to me. Since no picture is provided, it is important to know how the angle of 60o 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
 
  • #4
TSny
Homework Helper
Gold Member
13,086
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Ah. Note that the 60o shown in the figure is not the angle of incidence.
 
  • #5
Ah. Note that the 60o 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.
 

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