The mirror of length 2 λ meter makes 10 revolutions per minute about the axis crossing its mid point O and perpendicular to the plane of the figure. There are a light source in point A & an observer in point B of the circle of radius R meter drawn around centre O ( ∠ AOB = 90º)
(i) At what speed does the virtual image of A move?
Text Solution
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Ans.
(i)
Sol. Angular velocity of image = 2 ω mirror
= 
rad /sec.
= 
radian/sec
speed of image = ω R
= 
R m/sec
(ii)
Sol.
∠ OCB = 45º
∴ Sin rule
= 
= R 
= λ × 2
= 
= 
(iii)
Sol.
∠ OBC = 
= Ψ′ – 45º
Sine rule ∠ OCB = 135º
= 
⇒ 
= 
Sin( Ψ′ – 45) = 
Ψ′ – 45 = 30º
Ψ′ = 75º
Mirror is rotated by 75 – 15 = 60º
Speed of mirror = 120º/sec
So it will take 
sec to rotate by 60º.
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