What would the angle φ be for this deflected laser beam?

[aracali]

Homework Statement

The mirror in the image below deflects a horizontal laser by angle θ. What is the angle φ if θ = 60°.

Homework Equations

θ_i=θ_r

The Attempt at a Solution

So I know that, if I draw a line normal to the mirror, that will make it so that the incident angle and the reflected angle equal 60° (since 180-60=120 and the 2 angles have to be the same, so 120/2=60) but after that, I have no idea what to do. I know the angle is 30°, but how did they get that angle. Maybe I just need to reviw my geometry.

 

[Simon Bridge]

Draw the normal to the mirror and identify the angle of incidence and the angle of reflection.
[Edit] ... also derive the equation rrlating the angles first, then plugbin the numbers

Take care with notation.

 

[NascentOxygen]

Yes, you'll get nowhere without your junior high geometry. Relationships expressed concisely as "co-interior angles are supplementary", or maybe use "alternate angles are equal".

 

[Elsi b]

You can use the snell’s law of refraction with this formula: https://www.gstatic.com/education/formulas2/355397047/en/snell_s_law.svg

 

[Steve4Physics]

You can use the snell’s law of refraction with this formula: https://www.gstatic.com/education/formulas2/355397047/en/snell_s_law.svg

The question is about reflection, not refraction.

 

[Steve4Physics]

We don’t need no stinkin’ normals. (See note below.) All we need is a suitable diagram…

This immediately shows that θ = 2Φ.

I think I've told you too much. But can you explain why the marked angles in the diagram are equal to Φ?

Note.
To understand the opening sentence, you would need already to be familiar with the original reference. (Replace ‘normals’ by ‘badges’ and do a search, if you have nothing better to do!)

 

[jim mcnamara]

This is an ancient thread ... just pointing this out since the OP last logged in about a year ago.

 

[Elsi b]

yes it has to do with reflection angles:
E=180
P vertical=90
and we have 60 degree
The unknown angle is = 180 - 90 - 60 = 30 degrees

 

[kuruman]

This is an ancient thread ... just pointing this out since the OP last logged in about a year ago.

I would call it a zombie thread. Once revived, it acquires a strange life of its own. Only mentors possesses the awesome powers to kill it for good. Hint, hint.