a ray of light reflected from a plane mirror makes an angle of 60degree with the incident ray. If the mirror is turned so that the reflected ray makes an angle of 20degree with the same incident ray the mirror has been turned through an angle of ____? Why?
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The general rule is that
(1) Angle of Incidence = Angle of Reflection
as measured from a line normal to the mirror
Draw a picture, and you will see then that:
(2) Ai + Ar = Abt,
where
Abt = the angle between Ai and Ar
Since Ai = Ar,
(3) 2 * Ai = Abt ==>
From (3), you can see that a change of 1 degree in Ai gives a change in 2 degrees in Abt:
(5) ΔAbt = 2 ΔAi
Also, by definition, a change of 1 deg in the angle of the mirror Am results in a change of 1 degree in Ai:
(6) ΔAi = ΔAm
Substituting (6) in (5),
(7) ΔAbt = 2 ΔAm
Therefore, plugging in the stated problem:
(8) 60 - 20 = 2 ΔAm ===>
(9) ΔAm = 40 / 2 = 20 degree angle the mirror has been turned through.
.
(1) Angle of Incidence = Angle of Reflection
as measured from a line normal to the mirror
Draw a picture, and you will see then that:
(2) Ai + Ar = Abt,
where
Abt = the angle between Ai and Ar
Since Ai = Ar,
(3) 2 * Ai = Abt ==>
From (3), you can see that a change of 1 degree in Ai gives a change in 2 degrees in Abt:
(5) ΔAbt = 2 ΔAi
Also, by definition, a change of 1 deg in the angle of the mirror Am results in a change of 1 degree in Ai:
(6) ΔAi = ΔAm
Substituting (6) in (5),
(7) ΔAbt = 2 ΔAm
Therefore, plugging in the stated problem:
(8) 60 - 20 = 2 ΔAm ===>
(9) ΔAm = 40 / 2 = 20 degree angle the mirror has been turned through.
.
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1st case, angle i = 30 degree,
second case, angle i = 10 degree
so mirror is turned by 30-20
= 10 degree
second case, angle i = 10 degree
so mirror is turned by 30-20
= 10 degree