A particle is oscillating on the X-axis with an amplitude 2cm about the point x0=10cm with a frequency ω. A concave mirror of focal length 5cm is placed at the origin (see figure). Identify the correct statements: (A) The image executes periodic motion (B) The image executes non-periodic motion (C) The turning points of the image are asymmetric w.r.t the image of the point at x=10cm (D) The distance between the turning points of the oscillation of the image is 100/21<p></p>

For mean , → 1/u + 1/v = 1/f → 1/v = 1/10 -1/5[1/2] → 1/v = -1/10 → v = -10cm
As image copies the time period of object (A) is right as well. It will be periodic motion.
For one extreme → 1/u + 1/v = 1/f → 1/v = 1/8 - 1/5 → 1/v = -3/40 Rightarrow v = -40/3 cm
For other extreme → 1/u + 1/v = 1/f → 1/v = 1/12 - 1/5 → 1/v = -7/60 cm → v = -60/7cm
These points are asymmetric about x0=10cm
So, (c) is right.
Amplitude of oscillation of image → 40/3 - 60/7 → 10[40/3 - 60/7]10 × 10/21 → 100/21cm
(D) is right

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