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 .

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 ., (ii, iii), (i, iii, iv), (i, iv), (ii, iv)

MARKS App · Accepted Answer

Recall the proper formula of mirror formula, 1 f = 1 v + 1 u , given f = - 10 cm and u = - 5 cm then the formula of the concave mirror, - 1 10 = 1 v - 1 5 ⇒ 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, ⇒ - 1 8 + 1 v = 1 - 5 ⇒ v = - 40 3 cm , right arrow. For other extreme, ⇒ - 1 12 + 1 v = 1 - 5 ⇒ v = - 7 60 cm . These points are asymmetrical about x 0 = 10 cm . Now amplitude of oscillation of image, ⇒ 40 3 - 60 7 = 100 21 cm .

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