🔙 Prerequisite Revision:
👉 Chapter 9: Ray Optics (Mirrors, Lenses & Instruments)Chapter 10: Wave Optics
Vol 1: The Wave Nature & Huygens' Principle
Introduction: Ray optics fails to explain phenomena like Interference, Diffraction, and Polarization. These can only be explained if we treat light as a Wave.
- Spherical Wavefront: From a point source.
- Cylindrical Wavefront: From a line source (slit).
- Plane Wavefront: Small part of a spherical wavefront at large distance.
Huygens' Principle
A geometric method to find the shape of a wavefront at any instant.
- Every point on a given wavefront acts as a fresh source of new disturbance, called secondary wavelets, which travel in all directions with the speed of light.
- A surface touching these secondary wavelets tangentially in the forward direction at any instant gives the new wavefront at that instant.
Reflection & Refraction (Wave Theory Proof)
1. Snell's Law (Refraction):
Using Huygens' principle, we can derive: $\frac{\sin i}{\sin r} = \frac{v_1}{v_2} = \frac{n_2}{n_1}$.
2. Law of Reflection:
Using geometry of wavefronts, we can prove: $\angle i = \angle r$.
Vol 2: Interference of Light & YDSE
Superposition Principle: When two or more waves overlap, the resultant displacement is the vector sum of individual displacements.
(Note: Two independent bulbs can never be coherent).
Young's Double Slit Experiment (YDSE)
Thomas Young demonstrated interference using two slits $S_1$ and $S_2$.
| Condition | Constructive (Bright Fringe) | Destructive (Dark Fringe) |
|---|---|---|
| Path Difference ($\Delta x$) | $n\lambda$ $(n=0, 1, 2...)$ |
$(2n-1)\frac{\lambda}{2}$ $(n=1, 2...)$ |
| Phase Difference ($\phi$) | $2n\pi$ | $(2n-1)\pi$ |
The distance between two consecutive bright or dark fringes.
$$\beta = \frac{\lambda D}{d}$$
Vol 3: Diffraction (Single Slit)
Definition: The bending of light around the corners of an obstacle or aperture into the region of geometrical shadow.
Condition: Size of aperture ($a$) $\approx$ Wavelength ($\lambda$).
Single Slit Experiment
Produces a broad central maximum and alternate secondary minima and maxima.
- Condition for Minima (Dark): $a \sin \theta = n\lambda$
- Width of Central Maximum: $W = \frac{2\lambda D}{a}$
• Interference: All bright fringes are of equal intensity.
• Diffraction: Intensity decreases rapidly as we move away from the central maximum.
Vol 4: Polarization of Light
Phenomenon: Restricting the vibrations of a light wave to a single plane.
Significance: Polarization proves that light waves are Transverse in nature. (Sound waves cannot be polarized).
Malus' Law
When completely plane polarized light passes through an analyzer, the intensity ($I$) varies as:
($\theta$ is the angle between polarizer and analyzer axes).
Vol 5: Mission 100 Question Bank
Section A: MCQs
Q1. Which phenomenon shows that light is a transverse wave?
(a) Reflection (b) Interference (c) Diffraction (d) Polarization
Ans: (d) Polarization.
Q2. In YDSE, if the separation between slits is halved, the fringe width will:
(a) Double (b) Halve (c) Quadruple (d) Remain same
Ans: (a) Double ($\beta \propto 1/d$).
Section B: Numericals (High Probability)
Q3. In a YDSE, the slits are separated by 0.28 mm and the screen is placed 1.4 m away. The distance between the central bright fringe and the fourth bright fringe is 1.2 cm. Determine the wavelength of light used.
Solution:
Given: $d = 0.28$ mm, $D = 1.4$ m, $x_4 = 1.2$ cm, $n=4$.
Formula: $x_n = \frac{n \lambda D}{d} \Rightarrow \lambda = \frac{x_n d}{n D}$
$\lambda = \frac{1.2 \times 10^{-2} \times 0.28 \times 10^{-3}}{4 \times 1.4}$
$\lambda = 6 \times 10^{-7}$ m = 600 nm.
Ans: 600 nm.
Section C: Conceptual
Q4. Two independent light sources cannot produce interference. Why?
Ans: Because they are Incoherent. The phase difference between them changes randomly with time ($10^8$ times/sec), so no sustained interference pattern is formed.
Mission 100 Physics Series
Next Chapter: Dual Nature of Radiation & Matter (Modern Physics Begins!)
No comments:
Post a Comment