Ray Optics

JEE Main level, numerical answer, medium

86 of 295

Question 86 of 295

A fish rising vertically upward with a uniform velocity of 8ms–1,8m{s}^{–1}, observes that a bird is diving vertically downward towards the fish with the velocity of 12ms–1.12m{s}^{–1}. If the refractive index of water is 43,\dfrac{4}{3}, then the actual velocity of the diving bird to pick the fish, will be__________m{s}^{-1}.

Show answer and solution

Answer: 3

Let the fish be at a depth xx from the surface and let the bird be at height yy from the surface. So, with respect to fish
y′=μy+x⇒y′=4y3+xy'=\mu y+x \Rightarrow y'=\dfrac{4y}{3}+x
Differentiating with respect to time,
dy′dt=4dy3dt+dxdt\dfrac{dy'}{dt}=\dfrac{4dy}{3dt}+\dfrac{dx}{dt}
⇒4y3+dxdt=−12\Rightarrow \dfrac{4y}{3}+\dfrac{dx}{dt}=-12
⇒43⋅dydt=−12+8=−4\Rightarrow \dfrac{4}{3}\cdot \dfrac{dy}{dt}=-12+8=-4
⇒dydt=−3ms−1\Rightarrow \dfrac{dy}{dt}=-3m{s}^{-1}

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 (Refraction of light from plane surface), with the answer and a step-by-step solution. Scan a question from your own book or paper to get a whiteboard video.