PiTheory

PiTheory JEE Physics Practice & Revision Pack · Class 12 · Chapter 10 · JEE Main

Wave Optics

Chapter-wise practice and revision for JEE Main: concise notes on wavefronts and Doppler shift, Young's double slit (fringes, intensity, sheets and thin films), single-slit diffraction and resolving power, and polarisation, concept figures, and 51 selected previous-year JEE Main questions covering the major concepts and question patterns, each with a step-by-step solution.

51 selected questions4 topics3 concept figuresPreview · first 3 of 51 questions

How to study this chapter

  1. Look at the topic's figures, then read its notes (5 to 10 minutes). They give the major equations and methods the questions use.
  2. Solve the topic's questions with a timer: 2 minutes for Easy, 3 to 4 for Medium and Hard.
  3. Check the solution. Read the Point to note line even if you were right: it is the idea you will reuse.
  4. Mark each question Got it or Revise. Come back to the Revise list after two days.

Where the marks come from

Main idea of each of the 140 previous-year JEE questions in the PiTheory bank

YDSE86
Diffraction25
Polarisation23
Wavefronts6

Contents

  1. 1Wavefronts, Huygens' principle and Doppler shiftQ1–Q5
  2. 2Interference and Young's double slitQ6–Q31
  3. 3Single-slit diffraction and resolving powerQ32–Q43
  4. 4Polarisation, Malus's law and Brewster's angleQ44–Q51
  5. ✓Last-day checklist
01

Topic 1 · Q1–Q5

Wavefronts, Huygens' principle and Doppler shift

6 of the 140 JEE PYQs in the bank test this as their main idea

Quick notes

$$\text{rays}\perp\text{wavefronts},\qquad \frac{\Delta\lambda}{\lambda}=\frac{v}{c}\quad(v\ll c)$$

Every point of a wavefront is a source of secondary wavelets; the new wavefront is their common tangent. Huygens' construction gives the laws of reflection and refraction, with $\dfrac{\sin i}{\sin r}=\dfrac{v_1}{v_2}$.

  • Point source: spherical; line source (slit): cylindrical; far away or source at a lens focus: plane.
  • Plane $ax+by+cz=$ const travels along $(a,b,c)$.
  • Receding source: red shift ($\lambda$ increases); approaching: blue shift.
Trap. A tiny pinhole turns a plane wave into a spherical one; a wide slit barely changes it.

Practice: first 3 of 5 questions

Q1JEE Main 2024 (5 Apr, Shift 1)Easy

Light emerges out of a convex lens when a source of light is kept at its focus. The shape of the wavefront of the light is

  1. Aboth spherical and cylindrical
  2. Bplane
  3. Cspherical
  4. Dcylindrical
Answer and solution

Answer: Option B: plane

Concept. Rays from a point at the focus leave a convex lens parallel to the axis. Parallel rays have wavefronts perpendicular to them: flat planes.

Answer. Plane (Option B).

Point to note. Parallel rays: plane.

Q2JEE Main 2025 (2 Apr, Shift 1)Easy

A light wave is propagating with plane wavefronts of the type $x + y + z = \text{constant}$. The angle made by the direction of wave propagation with the $x$-axis is:

  1. A$\cos^{-1}\left(\dfrac{1}{\sqrt3}\right)$
  2. B$\cos^{-1}\left(\dfrac{2}{3}\right)$
  3. C$\cos^{-1}\left(\dfrac{1}{3}\right)$
  4. D$\cos^{-1}\left(\sqrt{\dfrac{2}{3}}\right)$
Answer and solution

Answer: Option A: $\cos^{-1}\left(\dfrac{1}{\sqrt3}\right)$

Concept. The wave travels along the normal to its wavefronts. For the plane $x+y+z=$ const the normal is $\hat i+\hat j+\hat k$.

Step 1. Unit vector. $\dfrac{\hat i+\hat j+\hat k}{\sqrt3}$.

Step 2. Angle with $x$. $\cos\theta=\dfrac{1}{\sqrt3}$.

Answer. Option A.

Point to note. Normal to the plane.

Q3JEE Main 2026 (28 Jan, Shift 1)Easy

Given below are two statements :

**Statement I :** A plane wave after passing through prism remains as plane wave but passing through small pin hole may become spherical wave.

**Statement II :** The curvature of a spherical wave emerging from a slit will increase for increasing slit width.

In the light of the above statements, choose the correct answer from the options given below :

  1. ABoth Statement I and Statement II are false
  2. BBoth Statement I and Statement II are true
  3. CStatement I is true but Statement II is false
  4. DStatement I is false but Statement II is true
Answer and solution

Answer: Option C: Statement I is true but Statement II is false

Concept. A prism only bends a plane wave, keeping it plane. A very small opening acts as a point source of secondary wavelets, so it gives a spherical wave. A wider slit diffracts less, so the emerging wave is flatter.

Step 1. Statement I. True.

Step 2. Statement II. A wider slit gives less curvature, not more: false.

Answer. Option C.

Point to note. Wide slit: less curvature.

48 more questions and 3 more topics in the full chapter

  1. 2Interference and Young's double slit26 questions with solutions
  2. 3Single-slit diffraction and resolving power12 questions with solutions
  3. 4Polarisation, Malus's law and Brewster's angle8 questions with solutions
  4. ✓Last-day checklist

The complete Wave Optics chapter is in the Class 12 Pack and the Complete Pack, as a PDF on WhatsApp. Want to see a whole chapter first? Laws of Motion and Current Electricity are free in full.

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