Is there a shortcut for finding theta4 using Snell's Law when theta2 is known?

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Discussion Overview

The discussion revolves around finding a method to determine the exit angle (theta4) using Snell's Law when the incident angle (theta2) is known, particularly in the context of a prism with a known apex angle. Participants explore relationships between the angles involved and the application of Snell's Law.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant inquires about a direct formula to find theta4 from theta1, given the apex angle, and expresses difficulty in transitioning from theta2 to theta3.
  • Another participant suggests considering the triangle formed by theta2 and theta3, indicating that the third angle is 180 minus the apex angle, leading to a relationship between theta2 and theta3.
  • A participant questions the assertion about the third angle being 180 minus the apex angle, proposing instead that the apex angle equals the sum of theta2 and theta3.
  • There is a suggestion that the normal lines are parallel to the rays, which raises further questions about the geometry involved.
  • Another participant confirms the relationship between theta2 and theta3 as apex = theta2 + theta3 but seeks clarification on how these angles relate to the triangle formed by the prism and the light ray.
  • A later reply acknowledges the previous misunderstanding and confirms that 180 minus the apex angle is indeed the third angle in the triangle formed by theta2 and theta3, suggesting the use of Snell's Law twice to find theta4.
  • One participant concludes that they have figured out the relationship, stating theta3 = A - theta2, and suggests applying Snell's Law again to find theta4.

Areas of Agreement / Disagreement

Participants express differing views on the relationships between the angles and the application of Snell's Law. There is no consensus on the correct interpretation of the angles or the best method to find theta4, indicating that multiple competing views remain.

Contextual Notes

There are unresolved assumptions regarding the geometry of the prism and the orientation of the normal lines, which may affect the relationships discussed. The dependence on specific conditions of the incoming ray is also noted but not fully explored.

glyon
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Snells Law prism - from theta2 -> theta3?

Hi, I was wondering if there's a formula to go straight from theta1 to theta 4, when the apex angle is known. Thanks[PLAIN]http://cord.org/cm/leot/course06_mod07/Fig3.gif

My problem is getting from theta2 to theta3.

Thanks

ps. This is not a homework question, i didnt even take physics in school when i had the chance!
 
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Consider the triangle with the angles theta2 and theta3, the one with two dotted sides and the third side made by the light ray in the prism.
The third angle in this triangle is 180-A. (To see that is so, consider the quadrilateral made by the two normals and the sides of the prism).
This will give you the relation between theta2 and theta3.
 
Thanks for getting back to me.

However, I'm still struggling to see how that third angle is 180-apex. I believe that the relationship between theta2 and theta3 is simply the apex = theta2 + theta3 but I can't see why!

Thanks again!
 
PLEASE DISREGARD - See next comment.

First off, by looking at the drawing, I am assuming the Normal lines are || to the rays and not perp. If they are perp then by definition theta 1 = theta 4 = 90.

theta 1 = theta2 + beta = theta 3 + gamma = theta 4

You don't need A. It does nothing for you. 180-A does not equal the third angle in the theta 2-3 triangle except for one frequency of the incoming ray. Sigma is dependent on multiple factors. The angle A is only one of those.

PLEASE DISREGARD - See next comment.
 
Last edited:
Pyle said:
First off, by looking at the drawing, I am assuming the Normal lines are || to the rays and not perp.

Thanks!

Aren't the normal line perpendicular to the prism edges rather than parallel to the rays though?

Basically all i want to know is the exit angle for a set incident angle, n1 and n2.
 
glyon said:
I believe that the relationship between theta2 and theta3 is simply the apex = theta2 + theta3 but I can't see why!

Consider the triangle bounded by the sides of the prism at the top, and the light ray through the prism at the bottom. One of its angles is A. The other two angles aren't labeled, but they're related to \theta_2 and \theta_3 (how?). What do those three angles add up to?
 
Oops,
Wasn't paying attention.
180-A is the third angle in the theta 2-3 triangle.
Just run it through Snell's law twice.

Sorry nasu, I was hasty.
 
Thanks,

I think I figured it out now:

theta3 = A - theta2, then do snells law again for theta4.
 
Last edited:

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