Ray Optics

JEE Main level, single correct, medium

47 of 295

Question 47 of 295

A particle is oscillating on the xx-axis with an amplitude 2cm2cm about the point x0=10cm{x}_{0}=10cm with a frequency. A concave mirror of focal length 5cm5cm 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=10cmX=10cm.
(iv) The distance between the turning points of the oscillation of the image is 10021cm\dfrac{100}{21}cm.

Show answer and solution

Answer: (B) (i, iii, iv)

Recall the proper formula of mirror formula, 1f=1v+1u\dfrac{1}{f}=\dfrac{1}{v}+\dfrac{1}{u}, given f=−10cmf=-10cm and u=−5cmu=-5cm then the formula of the concave mirror, −110=1v−15⇒v=−10cm-\dfrac{1}{10}=\dfrac{1}{v}-\dfrac{1}{5}\Rightarrow v=-10cm. As, image copies the time period of the object (A)\left(A\right) is right as well. It will be a periodic motion. For one extreme,
⇒−18+1v=1−5⇒v=−403cm\Rightarrow -\dfrac{1}{8}+\dfrac{1}{v}=\dfrac{1}{-5}\Rightarrow v=-\dfrac{40}{3}cm, right arrow.
For other extreme,
⇒−112+1v=1−5⇒v=−760cm\Rightarrow -\dfrac{1}{12}+\dfrac{1}{v}=\dfrac{1}{-5}\Rightarrow v=-\dfrac{7}{60}cm. These points are asymmetrical about x0=10cm{x}_{0}=10cm. Now amplitude of oscillation of image, ⇒403−607=10021cm\Rightarrow \dfrac{40}{3}-\dfrac{60}{7}=\dfrac{100}{21}cm.

JEE Main question paper PDF

Open a shift to read the full paper on this page, or download it.

JEE Main 2025 Apr 2 Shift 1 question paper

Open Download PDF

Opening paper…

Explain it as a whiteboard videoStep-by-step, in Hinglish or English. Your first video needs no login.Solved it on paper but got it wrong?Upload a photo of your working. Mistake Doctor marks the exact line that broke.
See it move: Lens ray diagram simulationDrag the sliders and watch the numbers in this question change.Revise Ray Optics firstFormula sheet, solved examples and the traps students fall into.

More Physics practice

JEE Main Physics practice question on Ray Optics (Mirror Formula, Reflection in Spherical Mirror), with the answer and a step-by-step solution. Scan a question from your own book or paper to get a whiteboard video.