Who answers this question is a genius!! PLEASE ANSWER IT!!?

Question

If you have two flat mirrors with an angle between them, a ray of light reflects from an object and onto the first mirror in a line (parallel to the second mirror) to the second mirror, then the ray reflects from it (the 1st mirror) to the second mirror, which reflects it again in a parallel line (according to the first mirror), and away. What's the angle between the two mirrors???!!?!?!

this question came in my physics exam and i don't know if i got it right!!!

Answer 1

60 degrees? (I'm a genius!)

Draw a diagram - let the angle be 'a'. To satisfy the parallel conditions you will see that the angle is repeated - when you establish that 3a is the sum of the angles within a triangle you can get the value of a (180/3). It is a combination of trig and knowing the properties of reflecting planes. Is this the answer you got?

It is important to know that the light beam and one of the mirrors are parallel, because you can then find the complementary  as well as the similar angles. It is also useful to know that the angle of the mirrors is the same as the incidence angle to the mirror, when it comes to setting out the direction of the reflected beam. Try drawing it out, and you should see what I mean.

No scanner so can't send diagram - but here's how:

1 Draw mirror 1 and 2 so they meet at angle 'a'

2 Label end of one mirror A, the point where they join B, and the end of other mirror C.

3 Draw light ray - parallel to AB  which meets BC at point D.

4 Ray is then reflected  from BC to meet line AB at point E

5 This is then reflected from AB and is parallel to BC - if you have this right it will cross the original light ray. Call this point F.

Now you can see that several of the angles are the same, and are each equal to angle 'a'. Fill these angles wth the letter 'a' as you go:

Angle ABC = AEF (Because EF and BC are parallel)

Angle AEF = BED (as it is a reflection);

and that

Angle AEF = EFD (because AB and DF are parallel)

Angle EFD = FDC (because EF and BC are parallel).

and that

Angle  FDC = BDE (because it is a reflection).

Now:

Consider the triangle BDE.  

Each angle is 'a' - as determined from above.

The sum of the angles is thus 3a, which is equal to 180 degrees (true for any triangle).

Each angle is one third of 180 degrees = 60 deg.

Therefore angle between mirrors (ABC) is equal to 60 deg.

QED.