A particle is oscillating on the x -axis with an amplitude 2 cm about the point x 0 = 10 cm with a frequency. A concave mirror of focal length 5 cm is placed at the origin (see figure). Identify the c

Question

A particle is oscillating on the x -axis with an amplitude 2 cm about the point x 0 = 10 cm with a frequency. A concave mirror of focal length 5 cm is placed at the origin (see figure). Identify the correct statements? (i) The image executes periodic motion. (ii) The image executes non-periodic motion. (iii) The turning points of the image are asymmetric with respect to the image of the point at X = 10 cm . (iv) The distance between the turning points of the oscillation of the image is 100 21 cm .

TestHub · Accepted Answer

Recall the proper formula of mirror formula, $\frac{1}{f} = \frac{1}{v} + \frac{1}{u}$ , given $f = - 10 cm$ and $u = - 5 cm$ then the formula of the concave mirror, $- \frac{1}{10} = \frac{1}{v} - \frac{1}{5} \Rightarrow v = - 10 cm$ . As, image copies the time period of the object $(A)$ is right as well. It will be a periodic motion. For one extreme,

$\Rightarrow - \frac{1}{8} + \frac{1}{v} = \frac{1}{- 5} \Rightarrow v = - \frac{40}{3} cm$ , right arrow.

For other extreme,

$\Rightarrow - \frac{1}{12} + \frac{1}{v} = \frac{1}{- 5} \Rightarrow v = - \frac{7}{60} cm$ . These points are asymmetrical about $x_{0} = 10 cm$ . Now amplitude of oscillation of image, $\Rightarrow \frac{40}{3} - \frac{60}{7} = \frac{100}{21} cm$ .

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