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## Homework Statement

Light consisting of a mixture of red and blue light enters a 40°, 70°, 70° prism along a line parallel to the side opposite the 40° vertex. The index of refraction of the prism material for blue light is 1.530, and for red light it is 1.525. What is the angle between the two emerging beams of light?

## Homework Equations

[itex]n_{1}*sin(Θ_{1}) = n_{2}*sin(Θ_{2})[/itex]

[itex]n_{red} = 1.525[/itex]

[itex]n_{blue} = 1.530[/itex]

[itex] ∆Θ = Θ_{blue} - Θ_{red}[/itex]

## The Attempt at a Solution

This is dispersion, so the incident light creates two refracted light rays. So, by Snell's Law

[itex] n*sin(Θ) = n_{red}*sin(Θ_{red}) [/itex]

[itex] n*sin(Θ) = n_{blue}*sin(Θ_{blue}) [/itex]

Now here's the part I'm not entirely sure about but decided to go with anyways:

I

*assumed*[itex] Θ = 70^{°} [/itex] was the angle of incidence and that the index of refraction of the prism is the same as glass [itex] n = 1.52 [/itex]

Plugging in I get

[itex]Θ_{blue} = 69.5^{°}[/itex]

[itex]Θ_{red} = 69.0^{°}[/itex]

Therefore,

[itex] ∆Θ = 0.5^{°}[/itex]

which is one of the answers! But...I'm not too confident about this result because I only

*assumed*what Θ was and what the index of refraction of the prism was without exactly knowing

*why*. So even if my answer's right I still don't completely understand what I did.

Could anyone help me out with this?