A particle is oscillating on the x-axis with an amplitude 2 cm about the point x₀=10 cm, with a frequency ω. A concave mirror of focal length 5 cm is placed at the origin (see figure). Identify the correct statements. (1) The image executes periodic motion. (2) The image executes non-periodic motio…

Question

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

Accepted Answer

(3) 1, 3, 4. Object moves between x=8 cm and x=12 cm, f=-5 cm; v=(uf)/(u-f). u=-8: |v|=(40)/3=13.33 cm. u=-12: |v|=(60)/7=8.57 cm. u=-10: |v|=10 cm. Image repeats with the object's period: periodic (1 true, 2 false). 13.33-10=3.33 but 10-8.57=1.43: asymmetric (3 true). Separation (40)/3-(60)/7=(100)/(21) cm (4 true).

Step-by-step solution

Why the other options are wrong