Ray reflecting off intersecting mirrors

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In summary, the conversation discusses the concept of multiple reflections when the angle of incidence, represented by γ, is less than 0. The individual does not understand how a negative angle is possible and asks for clarification. The expert responds by suggesting to draw a diagram with a small angle theta to better understand the concept. After further discussion, it is clarified that the law of reflection states that the angle of incidence is equal to the angle of reflection. However, the individual's diagram for the second reflection does not align with this law, leading to further confusion and a request for a new diagram.
  • #1
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Homework Statement
Please see below
Relevant Equations
Please see below
For this problem,
1677384446103.png

The solution is,
1677384477316.png

1677384490654.png

I don't understand how if ## \gamma < 0## then there will be multiple reflections? I don't understand how ##\gamma## can be negative.

Many thanks!
 
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  • #2
Callumnc1 said:
I don't understand how if ## \gamma < 0## then there will be multiple reflections? I don't understand how ##\gamma## can be negative.

Many thanks!
Try drawing it with θ very small.
 
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  • #3
haruspex said:
Try drawing it with θ very small.
Thank you for your reply @haruspex!

Like this?
1677388295033.png

Many thanks!
 
  • #4
Callumnc1 said:
Thank you for your reply @haruspex!

Like this?
View attachment 322878
Many thanks!
First reflection looks fine, the second impossible. How do you figure out where a reflected ray goes?
 
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  • #5
haruspex said:
First reflection looks fine, the second impossible.
Thank you for your reply @haruspex!

How do you figure out where a reflected ray goes?

Using the law of reflection

EDIT: Apologies, the diagram is not to scale. Let me know if you want me to redo it and I will use a better program (Microsoft paint instead of snip tool)

Many thanks!
 
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  • #6
Callumnc1 said:
Using the law of reflection
Which states …?
 
  • #7
Thank you for your reply @haruspex!

Angle of incidence is equal to angle of reflection

Many thanks!
 
  • #8
Callumnc1 said:
Thank you for your reply @haruspex!

Angle of incidence is equal to angle of reflection

Many thanks!
But what you drawn for the second reflection is nothing like that.
Draw the normal to the mirror where the ray hits it. The incident ray makes some angle theta to that normal. The reflected ray should also make angle theta to the normal, but on the other side of the normal.
 
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  • #9
haruspex said:
But what you drawn for the second reflection is nothing like that.
Draw the normal to the mirror where the ray hits it. The incident ray makes some angle theta to that normal. The reflected ray should also make angle theta to the normal, but on the other side of the normal.
Thank you for your reply @haruspex!

I will draw another diagram. Sorry if my replies are a bit slow

Many thanks!
 

FAQ: Ray reflecting off intersecting mirrors

What happens when a ray of light strikes the intersection point of two mirrors?

When a ray of light strikes the intersection point of two mirrors, it is reflected according to the law of reflection from the surface it encounters first. The ray will then continue to the second mirror, where it will reflect again according to the same law.

How do the angles of incidence and reflection change with intersecting mirrors?

The angles of incidence and reflection for each mirror are determined independently. For each reflection, the angle of incidence is equal to the angle of reflection, measured relative to the normal (perpendicular) to the mirror surface at the point of incidence.

Can the path of a reflected ray be predicted when dealing with intersecting mirrors?

Yes, the path of a reflected ray can be predicted using the laws of reflection. By knowing the angles and the arrangement of the mirrors, one can trace the ray's path through successive reflections, calculating each reflection point and angle step by step.

How does the angle between two intersecting mirrors affect the number of reflections?

The angle between two intersecting mirrors influences the number of reflections a ray undergoes before potentially exiting the mirror system. Smaller angles can lead to multiple reflections, while larger angles may result in fewer reflections. In some configurations, the ray may even become trapped in a continuous cycle of reflections.

What practical applications utilize the principles of ray reflection off intersecting mirrors?

Practical applications of ray reflection off intersecting mirrors include periscopes, kaleidoscopes, optical instruments, and certain types of laser systems. These applications leverage controlled reflections to manipulate light paths for various purposes, such as observation, image formation, and beam direction.

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