The figure shows an overhead view of a complicated set of mirrors arranged so that a laser ray can enter the enclosure at an angle of φ = 6.10° as measured from the horizontal, but exit parallel to the wall W, as shown. At what angle θ, measured from the horizontal, must the final mirror, M, be placed?

Question

The figure shows an overhead view of a complicated set of mirrors arranged so that a laser ray can enter the enclosure at an angle of φ = 6.10° as measured from the horizontal, but exit parallel to the wall W, as shown.  At what angle θ, measured from the horizontal, must the final mirror, M, be placed?

anonymous · Answer

@Cuanchi

anonymous · Answer

@agent0smith

anonymous · Answer

@ganeshie8

anonymous · Answer

@Rushwr

anonymous · Answer

@quinton1011

quinton1011 · Answer

let me think

anonymous · Answer

Alright

agent0smith · Answer

"The figure shows..." this is why no one has tried helping you...

anonymous · Answer

About to post the picture

anonymous · Answer

https://moodle.csc.tntech.edu/pluginfile.php/1948/question/questiontext/9135/2/2527/A10Q3%20%281%29.jpg

anonymous · Answer

@agent0smith  That's the picture that goes with it. Let me know if you're able to see it.

agent0smith · Answer

Take a screenshot. This should've been done when the question was posted 21 hours ago, though...

anonymous · Answer

@agent0smith  Forgot. Working on putting up the screen shot

anonymous · Answer

@agent0smith http://oi64.tinypic.com/2zqdi85.jpg

anonymous · Answer

Hopefully that one will work

agent0smith · Answer

Use the fact that angle of incidence = angle of reflection. It's just geometry, use triangles and such

anonymous · Answer

My geometry is rusty. Haven't had to use it in years.

anonymous · Answer

@agent0smith  So could you walk me through the steps please?

agent0smith · Answer

First use the fact that angle of incidence = angle of reflection, to find the first reflection angle. Draw it on paper. There's a lot of simple right triangles you can use.

anonymous · Answer

Alright. The angle of incidence for this arrow closest to W right?

agent0smith · Answer

Yes

anonymous · Answer

And then the reflection is the one that directly leads from incidence?

agent0smith · Answer

Yes

anonymous · Answer

And the angle for incidence = 6.10 deg? So that means reflection would be -6.10 deg?

agent0smith · Answer

Why would it be negative? If you're drawing it out as you go, negatives are not relevant.

anonymous · Answer

I thought it would need to be negative if it was on the other side. So that's not true. So it's just reflection = 6.10

anonymous · Answer

|dw:1458150709755:dw|

anonymous · Answer

Something like that?

agent0smith · Answer

Yes, now just keep solving for angles as you go from one mirror to the next. Use right triangles

anonymous · Answer

|dw:1458151088923:dw|