Wave Optics

JEE Main level, numerical answer, medium

14 of 191

Question 14 of 191

Two waves of intensity ratio 1:91:9 cross each other at a point. The resultant intensities at the point, when (a) Waves are incoherent is I1(b){I}_{1}\left(b\right) Waves are coherent is I2{I}_{2} and differ in phase by 60o{60}^{o}. If I1I2=10x\dfrac{{I}_{1}}{{I}_{2}}=\dfrac{10}{x}, then x=x= _________.

Show answer and solution

Answer: 13

For incoherent wave, I1=IA+IB⇒I1=I0+9I0{I}_{1}={I}_{A}+{I}_{B}\Rightarrow {I}_{1}={I}_{0}+9{I}_{0}
⇒I1=10I0\Rightarrow {I}_{1}=10{I}_{0}
For coherent wave I2=IA+IB+2IAIBcos⁡60o{I}_{2}={I}_{A}+{I}_{B}+2\sqrt{{I}_{A}{I}_{B}}\cos {60}^{o}
⇒I2=I0+9I0+29I02×12=13I0\Rightarrow {I}_{2}={I}_{0}+9{I}_{0}+2\sqrt{9I02}\times \dfrac{1}{2}=13{I}_{0}
⇒I1I2=1013\Rightarrow \dfrac{{I}_{1}}{{I}_{2}}=\dfrac{10}{13}
Therefore, x=13x=13.

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: Wave optics: YDSE, diffraction and polarisation simulationDrag the sliders and watch the numbers in this question change.

More Physics practice

JEE Main Physics practice question on Wave Optics (Interference of Light), with the answer and a step-by-step solution. Scan a question from your own book or paper to get a whiteboard video.