A plane mirror is rotated at 20 degree without affecting the angle of incidence.?

Question

the new angle between incident and reflected ray is found to be 45. what was the original angle between them?

Answer 1

85 degrees
let intial INCIDENCE angle be (pi) so reflected light will also be at (pi) from normal on OTHER side >>> because law of reflection >> angle i = angle r
initial angular separation = 2pi --------(1)
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after 20 deg rotation of normal of mirror
incid angle = (pi-20)
reflec angle = (pi-20)
given 45 = (pi-20) + (pi-20) = 2pi -40
2pi = 85
that is the earlier sepation of inci/reflecti (1)

Answer 2

Crabby is correct.

Whenever you rotate a plane mirror, the relected ray ALWAYS rotates through 2X the rotation angle.

the proof is trivial. Suppose you have some initial incident angle, A, with respect to the mirror's normal, then you rotate the mirror's normal by some amount, B degrees, so the new incident angle is A + B, and the new angle of reflection is also A + B.

Thus the initial angle between the incident and reflected rays was 2A, and after the rotation the angle between the incident and reflected rays is 2A + 2B the increase is 2X the rotaion angle.

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So in your problem is the rotation is 20 and the final angle between the rays is 45 then:

2A +2*20 = 45

2A = 5, where 2A is the angle between the incident and reflected rays.

Answer 3

I hope you mean that keeping the incident ray constant , the mirror is rottated through an angle 20 degree.

In that case

If I is the original angle of incidence then 2I is the angle between the original incident and reflected ray.

If mirror is turned through 20 degree, the normal to the mirror is turned through angle 20.

The angle of incidence is the angle between the normal and incident ray.

Hence ,the new incident angle is [I ± 20.]

The angle between the incident ray and new reflected ray is two times [I ± 20.]
= 2I ± 40

It is given that 2I ± 40 = 45

2I = 5 or 85 degree.

The original angle between incident and reflected ray is 2I.

Answer 4

Rotation Of Plane Mirror

Answer 5

First, make your right hand into fist form.Open the thumb and index finger(beside thumb).Make them perpendicular to each other. Make sure your palm is not facing you. Let your right thumb be a part of the plane mirror. The index finger is your normal.
So after plane is rotated, the incident ray comes at the angle 22.5deg since the angle between the two rays is 45deg.
Use your left index finger and put it between your right thumb and right index finger. Now without moving your left, rotate your right to the left by 20deg.So what is left is simply 22.5-20=2.5deg. Angle of incidence=angle of reflecT. So the angle between them is 5deg.

Answer 6

Ofcouse it will affect the angle of incident .The angle of incidence will be less that 45.so the original angle is 45-20=25.

Answer 7

Pl. tell me how to rotate the mirror without affecting the angle of incidence. If the angle of incidence is not affected, the angle of reflection also should not be affected.

Answer 8

I think it is 5 degrees