Finding a Mistake in My Sketch: Can I Get Emergent Beam Perpendicular to AB?

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Homework Help Overview

The discussion revolves around a sketch related to the behavior of light as it passes through a prism, specifically focusing on the conditions under which an emergent beam can be perpendicular to a specified face (AB) of the prism. Participants are analyzing the angles involved and the implications of total internal reflection.

Discussion Character

  • Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants are examining the angles in the sketch and questioning the assumptions made about the direction of the emergent beam and the conditions for total internal reflection. There is a focus on whether the incident ray can indeed be perpendicular to the face of the prism.

Discussion Status

There is an ongoing exploration of the implications of the angles described in the sketch. Some participants are providing clarifications regarding the assumptions about the diagram and the conditions for the emergent beam, while others are questioning the feasibility of the angles leading to a perpendicular emergent ray.

Contextual Notes

Participants are discussing the constraints of the problem as stated, particularly the requirement for the emergent beam to be perpendicular to face AB, and the implications of this requirement on the angles of incidence and refraction.

songoku
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Homework Statement
A light beam from a laser source which is parallel to a horizontal surface hits an equilateral prism as shown in the figure above. What is the angle α (between AB and horizontal) if the emergent beam is perpendicular to face AB? (refractive index of prism is 2)
a. 42.5 degree
b. 24.5 degree
c. 15.0 degree
d. 46.0 degree
e. 30.0 degree
Relevant Equations
Snell's law
Total internal reflection
Untitled.png

This is my sketch:

aaa.png

I think the only possible way to get emergent beam perpendicular to AB is when the incoming ray is refracted towards side AC then total internal reflection occurs as shown in my sketch.

Angle QAR = 60o and angle ARQ = 90o so angle AQR = 30o

It means angle CQP is also 30o so angle QPC = 90o, which is impossible

Where is my mistake? Thanks
 
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The diagram shows the ray emerging from AB, but the text does not say that.
Is that diagram as given to you, or did you make that assumption?
 
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songoku said:
... so angle QPC = 90o, which is impossible
Why is this impossible?
 
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haruspex said:
The diagram shows the ray emerging from AB, but the text does not say that.
Is that diagram as given to you, or did you make that assumption?
The question states : " if the emergent beam is perpendicular to face AB".

The first diagram is from question, the second is my own sketch

TSny said:
Why is this impossible?
Because it means that the angle of refraction when the lights travels from air to prism is zero degree, which can only be obtain if angle of incidence is also zero degree.

Or are you suggesting that actually the incident ray is perpendicular to side BC so this means that the prism is tilted as far as 30o?

Thanks
 
songoku said:
The question states : " if the emergent beam is perpendicular to face AB".
Yes, but that is just a direction. It does not say it emerges from that face.
songoku said:
The first diagram is from question.
Ok, so it does emerge from that face, in which case...
songoku said:
the incident ray is perpendicular to side BC so this means that the prism is tilted as far as 30o?
which is indeed one of the options.
 
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Thank you very much for the help haruspex and TSny
 

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