Wave Optics - What is, Types, Formulas, Topics

Wave Optics Class 12th Topics (NCERT Syllabus)

Topics of wave optics are given below:

1. Introduction

Ray optics explains many optical phenomena, but it cannot describe effects like interference, diffraction, and polarisation. These phenomena arise from the wave nature of light, which is studied under Wave Optics.

2. Huygens' Principle

Huygens proposed that every point on a wavefront acts as a source of secondary wavelets. The forward envelope of these wavelets gives the new wavefront. This principle helps in explaining the laws of reflection and refraction.

• Huygens' Principle

3. Refraction and Reflection of Plane Wave using Huygens' Principle

Using Huygens' construction, one can derive:

• Law of Reflection: Angle of incidence = Angle of reflection.
• Law of Refraction (Snell's law)
  $\frac{\sin i}{\sin r}=\frac{v_1}{v_2}=\frac{n_2}{n_1}$

4. Coherent and Incoherent Addition of Waves

• Coherent sources: Two sources having a constant phase difference and same frequency (essential for sustained interference).
• Incoherent sources: Sources with random phase difference; they do not produce sustained interference.

5. Interference of Light Waves - Young's Double Slit Experiment (YDSE)

When two coherent light waves overlap, they produce regions of constructive and destructive interference.

Fringe width:

$
\Delta x=\frac{\lambda D}{d}
$

where $\lambda=$ wavelength, $\mathrm{D}=$ distance of screen from slits, $\mathrm{d}=$ distance between slits.

Bright fringes: Path difference $=n \lambda$.

Dark fringes: Path difference $=(2 n+1) \frac{\lambda}{2}$.

• Interference of Light

6. Diffraction of Light

Diffraction is the bending and spreading of light waves around edges and apertures.

• In a single slit diffraction, the central maximum is the brightest and widest.
• Angular width of central maximum:
  $\theta=\frac{\lambda}{a}$
  where $a=$ slit width.

Diffraction of Light

7. Polarisation of Light

Light waves are transverse in nature. When the vibrations of the electric field are restricted to one direction, the light is said to be polarised.

• Methods: Reflection, scattering, polaroids.
• Uses: Sunglasses, 3D movies, stress analysis, and optical instruments.

Polarisation of Light

Wave Optics Real Life Application

Interference – Thin film colors, anti-reflective coatings.

Diffraction – Spectrometers, optical instruments.

Polarisation – Polaroid sunglasses, 3D movies.

Formulas For Wave Optics

1. Interference (Young's Double Slit Experiment - YDSE)
Path difference:

$
\Delta x=d \sin \theta \approx \frac{x d}{D}
$

Condition for constructive interference (bright fringe):

$
\Delta x=n \lambda
$

Condition for destructive interference (dark fringe):

$
\Delta x=\left(n+\frac{1}{2}\right) \lambda
$

Fringe width:

$
\beta=\frac{\lambda D}{d}
$

where $D=$ distance to screen, $d=$ slit separation, $\lambda=$ wavelength.
2. Diffraction (Single Slit)
Condition for minima:

$
a \sin \theta=n \lambda \quad(n=1,2,3 \ldots)
$

Angular width of central maximum:

$
\Delta \theta=\frac{2 \lambda}{a}
$

where $a=$ slit width.

3. Polarisation
Malus' Law:

$
I=I_0 \cos ^2 \theta
$

where $I_0=$ initial intensity, $\theta=$ angle between light's plane of vibration and polariser.
Brewster's Law:

$
\tan i_p=\mu
$

where $i_p=$ polarising angle, $\mu=$ refractive index.
4. Huygens' Principle (for refraction)
Snell's Law from Huygens:

$
\frac{\sin i}{\sin r}=\frac{v_1}{v_2}=\frac{\mu_2}{\mu_1}
$

Exam-wise Weightage of Wave Optics

Approach to Solve Wave Optics Questions

To solve Wave Optics questions, first identify the phenomenon involved-interference, diffraction, or polarisation. Then recall the main formula for that concept, like fringe width $\Delta y=\frac{\lambda D}{d}$ in Young's experiment, diffraction condition $a \sin \theta=n \lambda$, or Brewster's law $\tan \theta_B=\mu$. Always draw a simple diagram to visualize the wavefronts or fringes. While solving, convert units properly and use small angle approximations if needed. For board exams, focus more on derivations and diagrams, while for competitive exams like JEE and NEET, practice numericals and conceptual questions.

Recommended Books For Wave Optics

To lay a strong foundation in wave optics, begin by referring to the NCERT book for both theory and practice questions. This will help you develop a clear understanding of the fundamental concepts of wave optics ncert. Once you have completed the NCERT book, move on to the NCERT Exemplar book, which offers more challenging questions to further enhance your skills.

For those seeking more advanced level questions and a deeper exploration of wave optics, additional resources such as "Concepts of Physics" by H.C. Verma or "Understanding Physics" by DC Pandey can be beneficial. These books provide comprehensive coverage of the subject and present a wide range of practice problems.

Remember to consistently revise and practice the concepts and problems from these resources to strengthen your understanding and proficiency in wave optics.

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