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Physics Question on Ray optics and optical instruments

A flat mirror revolves at a constant angular velocity making 2 rev s−1.2\, rev\, s^{-1}. With what velocity will a light spot move along a spherical screen with a radius of 10 m10\, m, if the mirror is at a centre of curvature of the screen ?

A

251.2 ms−1251.2\, ms^{-1}

B

261.2 ms−1261.2\, ms^{-1}

C

271.2 ms−1271.2\, ms^{-1}

D

241.2 ms−1241.2\, ms^{-1}

Answer

251.2 ms−1251.2\, ms^{-1}

Explanation

Solution

Angular velocity of mirror =4πrads−1=4 \pi rad s ^{-1}
Angular velocity of reflected ray
=2×4π=8πrads−1=2 \times 4 \pi=8 \pi rad s ^{-1}
∴\therefore velocity of spot v=10×8πv=10 \times 8 \pi
=80×3.14=251.2 ms−1=80 \times 3.14=251.2\, ms ^{-1}