Ray Optics

JEE Main level, single correct, medium

48 of 295

Question 48 of 295

A particle is oscillating on the X\mathrm{X}-axis with an amplitude 2 cm2 \mathrm{~cm} about the point x0=10 cmx_0=10 \mathrm{~cm} with a frequency ω\omega. A concave mirror of focal length 5 cm\mathrm{cm} 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 xx =10 cm=10 \mathrm{~cm}
(D) The distance between the turning points of the oscillation of the image is 10021\frac{100}{21}

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Answer: (C) (A), (C), (D)

When object is at 8 cm8 \mathrm{~cm}
Image V1=f×uu−f=5×88−5=−403 cmV_1=\frac{\mathrm{f} \times \mathrm{u}}{\mathrm{u}-\mathrm{f}}=\frac{5 \times 8}{8-5}=-\frac{40}{3} \mathrm{~cm}
When object is at 12 cm12 \mathrm{~cm}
Image V2=f×uu−f=5×1212−5=−607 cm\mathrm{V}_2=\frac{\mathrm{f} \times \mathrm{u}}{\mathrm{u}-\mathrm{f}}=\frac{5 \times 12}{12-5}=-\frac{60}{7} \mathrm{~cm}
Separation =∣V1−V2∣=403−607=10021 cm=\left|\mathrm{V}_1-\mathrm{V}_2\right|=\frac{40}{3}-\frac{60}{7}=\frac{100}{21} \mathrm{~cm}
So A,C\mathrm{A}, \mathrm{C} and D\mathrm{D} are correct statements.

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