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

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SUMMARY

The discussion centers on the conditions required for an emergent beam to be perpendicular to face AB of a prism. The user identifies a mistake in their sketch, concluding that for the emergent beam to be perpendicular, the incident ray must be perpendicular to side BC, implying a tilt of the prism. The angles involved are clarified, with angle QAR at 60 degrees and angle ARQ at 90 degrees leading to a contradiction in angle QPC being 90 degrees. The participants confirm that the emergent beam's direction does not necessarily indicate it emerges from face AB.

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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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