πFull Physics Short Notes Part 4 | Class 12 & JEE 2026
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Ray Optics is a very important chapter in Class 12 Physics and competitive exams like JEE Main and NEET. It deals with the behavior of light when it travels in straight lines and interacts with mirrors, lenses, prisms, and optical instruments. Understanding this chapter helps students solve both theoretical and numerical questions effectively.
Wave Optics is the branch of optics that explains the behavior of light by treating it as a wave phenomenon. This chapter helps us understand important phenomena such as interference, diffraction, and polarization, which cannot be explained using ray optics alone. Wave optics is extremely important for CBSE Boards, JEE Main, and NEET examinations.✅ SECTION 1 - RAY OPTICS
π¦π 1. Reflection of Light
Reflection is the phenomenon in which light, after striking a surface, bounces back into the same medium. This happens because light cannot pass through opaque surfaces.
π Laws of Reflection
The incident ray, reflected ray, and the normal at the point of incidence all lie in the same plane, called the plane of incidence.
The angle of incidence is equal to the angle of reflection:
\[
\angle i = \angle r
\]
These laws apply to all reflecting surfaces, whether smooth or rough.
πͺπ 2. Object and Image
An object is a point from which light rays originate or appear to originate.
Real object: Rays actually diverge from it
Virtual object: Rays appear to diverge from it
An image is formed when reflected or refracted rays meet or appear to meet.
Real image: Formed by actual convergence of rays
Virtual image: Formed by apparent divergence of rays
π Image formation depends only on reflected or refracted rays, not on incident rays.
ππͺ 3. Plane Mirror
A plane mirror is a flat reflecting surface.
✨ Characteristics of Image
Image size is equal to object size
For a real object, image is virtual
Distance of image from mirror = distance of object from mirror
π Rotation of Plane Mirror
If a plane mirror is rotated by an angle ΞΈ, the reflected ray rotates by 2ΞΈ in the same direction.
π’πͺ 4. Number of Images in Inclined Mirrors
When two plane mirrors are inclined at an angle ΞΈ:
\[
m = \frac{360^\circ}{\theta}
\]
If m is even → number of images = \( m - 1 \)
If m is odd:
Object on angle bisector → \( m - 1 \)
Otherwise → \( m \)
If m is fractional → nearest even integer
π΅πͺ 5. Spherical Mirrors
Spherical mirrors are parts of a hollow sphere.
Types:
Concave mirror (converging)
Convex mirror (diverging)
π Mirror Formula
\[
\frac{1}{f} = \frac{1}{v} + \frac{1}{u}
\]
(Valid only for paraxial rays)
π Magnification
\[
m = -\frac{v}{u}
\]
Negative sign indicates inversion of image.
ππΈ 6. Velocity of Image
When an object moves along the principal axis, the image also moves.
\[
\frac{dv}{dt} = -\left(\frac{v^2}{u^2}\right)\frac{du}{dt}
\]
This relation is useful in numerical problems involving moving objects.
⚡π 7. Optical Power of Mirror
Optical power measures the converging or diverging ability of a mirror.
\[
P = -\frac{1}{f}
\]
Unit: Diopter (D)
Focal length must be in meters
ππ 8. Refraction of Light
Refraction is the bending of light when it passes from one medium to another due to change in speed.
π Laws of Refraction (Snell’s Law)
\[
\mu_1 \sin i = \mu_2 \sin r
\]
π Frequency of light remains constant during refraction.
π§±π 9. Refraction Through Glass Slab
When light passes through a parallel glass slab:
Emergent ray is parallel to incident ray
A lateral shift occurs
π Lateral Shift
\[
x = t \frac{\sin(i - r)}{\cos r}
\]
π️⬆️ 10. Apparent Depth
An object placed in a denser medium appears raised when viewed from a rarer medium.
\[
h' = \frac{h}{\mu}
\]
Apparent shift:
\[
\Delta x = t\left(1 - \frac{1}{\mu}\right)
\]
π₯π 11. Total Internal Reflection (TIR)
✅ Conditions
Light travels from denser to rarer medium
Angle of incidence > critical angle
π Critical Angle
\[
\sin C = \frac{1}{\mu}
\]
πΊπ 12. Refraction Through a Prism
Angle of deviation:
\[
\delta = i + i' - A
\]
At minimum deviation:
\[
\mu = \frac{\sin\left(\frac{A+\delta_{min}}{2}\right)}{\sin\left(\frac{A}{2}\right)}
\]
For thin prism:
\[
\delta = (\mu - 1)A
\]
ππ¬ 13. Dispersion of Light
Dispersion is the splitting of white light into its constituent colors.
Angle of dispersion:
\[
\theta = \delta_v - \delta_r
\]
Dispersive power:
\[
\omega = \frac{\delta_v - \delta_r}{\delta_y}
\]
⚪π 14. Refraction at Spherical Surface
\[
\frac{\mu_2}{v} - \frac{\mu_1}{u} = \frac{\mu_2 - \mu_1}{R}
\]
Magnification:
\[
m = \frac{\mu_1 v}{\mu_2 u}
\]
ππ 15. Lenses
π Lens Formula
\[
\frac{1}{v} - \frac{1}{u} = \frac{1}{f}
\]
π ️ Lens Maker’s Formula
\[
\frac{1}{f} = (\mu - 1)\left(\frac{1}{R_1} - \frac{1}{R_2}\right)
\]
⚡ Power of Lens
\[
P = \frac{1}{f}
\]
π¬π 16. Optical Instruments
π Simple Microscope
\[
M = 1 + \frac{D}{f}
\]
π¬ Compound Microscope
\[
M = \frac{v_0}{u_0}\left(1 + \frac{D}{f_e}\right)
\]
π Astronomical Telescope
\[
M = \frac{f_0}{f_e}
\]
π―π 17. Resolving Power
Microscope:
\[
\text{Resolving power} = \frac{2\mu \sin\theta}{1.22\lambda}
\]Telescope:
\[
\text{Resolving power} = \frac{a}{1.22\lambda}
\]
π§ π Summary: Ray Optics at a Glance
Ray optics deals with straight-line propagation of light.
Reflection follows two basic laws applicable to all mirrors.
Plane mirrors form virtual images of same size.
Spherical mirrors can form real or virtual images depending on object position.
Refraction occurs due to change in speed of light, not frequency.
Total internal reflection occurs only under specific conditions.
Prisms cause deviation and dispersion of light.
Lenses obey lens formula and lens maker’s formula.
Optical instruments increase angular magnification and resolving power.
✅ SECTION 2 - WAVE OPTICS
ππ¦ 1. Huygens’ Wave Theory
Huygens’ principle explains how light waves propagate through a medium.
According to this theory:
Every point on a wavefront acts as a source of secondary wavelets, which spread out in all directions.
These secondary wavelets travel with the same speed as light in that medium.
The new wavefront at any later time is obtained by drawing a tangent (forward envelope) to all the secondary wavelets.
In a homogeneous medium, the direction of propagation of light is always perpendicular to the wavefront.
This principle successfully explains the laws of reflection and refraction of light.
ππ 2. Wavefront
A wavefront is the locus of all points in a medium that are vibrating in the same phase at a given instant.
✨ Types of Wavefronts
πΉ Plane Wavefront
Formed when the source of light is very far away.
All rays are parallel to each other.
Example: Light coming from the Sun (approximately).
πΉ Spherical Wavefront
Formed when the light source is a point source.
Waves spread out equally in all directions.
ππ 3. Coherent and Incoherent Sources
✅ Coherent Sources
Two sources are said to be coherent if:
They produce light waves of the same frequency (same wavelength).
They maintain a constant phase difference.
Coherent sources are essential for producing sustained interference patterns.
❌ Incoherent Sources
Sources are incoherent if:
Their frequencies are different, or
Their phase difference changes continuously with time.
Interference patterns cannot be observed using incoherent sources.
ππ§ͺ 4. Interference of Light (Young’s Double Slit Experiment – YDSE)
Interference is the phenomenon of redistribution of light intensity due to the superposition of two coherent light waves.
π¬ Resultant Intensity
For coherent sources:
\[
I = I_1 + I_2 + 2\sqrt{I_1 I_2}\cos\phi
\]
For incoherent sources:
\[
I = I_1 + I_2
\]
π Intensity of light is proportional to:
Width of the slit
Square of amplitude
✨ Maximum and Minimum Intensity
Maximum intensity:
\[
I_{max} = (\sqrt{I_1} + \sqrt{I_2})^2
\]Minimum intensity:
\[
I_{min} = (\sqrt{I_1} - \sqrt{I_2})^2
\]
If \( I_1 = I_2 \):
Bright fringe intensity is maximum
Dark fringe intensity becomes zero
ππ 5. Position of Bright and Dark Fringes
π Bright Fringe
Path difference:
\[
\Delta = n\lambda \quad (n = 0, 1, 2, ...)
\]
Position of nth bright fringe:
\[
y_n = \frac{n\lambda D}{d}
\]
⚫ Dark Fringe
Path difference:
\[
\Delta = \frac{(2m - 1)\lambda}{2}
\]
Position of mth dark fringe:
\[
y_m = \frac{(2m - 1)\lambda D}{2d}
\]
Where:
D = distance between slit and screen
d = distance between slits
ππ 6. Fringe Width
Fringe width is the distance between two consecutive bright or dark fringes.
\[
\beta = \frac{\lambda D}{d}
\]
Angular fringe width:
\[
\theta = \frac{\lambda}{d}
\]
π§±π 7. Effect of Introducing a Thin Transparent Sheet
When a transparent sheet of refractive index \( \mu \) and thickness \( t \) is introduced in one path:
Optical path increases from \( t \) to \( \mu t \)
The entire fringe pattern shifts, but fringe width remains unchanged
Shift in fringe pattern:
\[
x = (\mu - 1)\frac{tD}{d} = (\mu - 1)\frac{t}{\lambda}\beta
\]
The shift occurs towards the side of the sheet.
π𧩠8. Diffraction of Light
Diffraction is the bending of light around obstacles or apertures whose size is comparable to the wavelength of light.
π Fraunhofer Diffraction (Single Slit)
Occurs when source and screen are effectively at infinity.
Light waves are plane waves.
❌ Condition for Minima
\[
a\sin\theta_n = n\lambda
\]
✨ Condition for Maxima
\[
a\sin\theta_n = \frac{(2n + 1)\lambda}{2}
\]
π Width of Central Maximum
Linear width:
\[
W = \frac{2\lambda D}{a}
\]
Angular width:
\[
W_\theta = \frac{2\lambda}{a}
\]
The central maximum is the brightest and widest.
ππ¦ 9. Polarization of Light
Polarization is the phenomenon in which vibrations of light waves are restricted to one plane.
Only transverse waves can be polarized, which proves that light is transverse in nature.
π₯π 10. Brewster’s Law
According to Brewster’s law:
\[
\mu = \tan\theta_p
\]
Where:
\( \theta_p \) is the Brewster angle (polarizing angle)
At Brewster angle:
Reflected and refracted rays are perpendicular to each other.
Reflected light becomes completely plane polarized.
ππ 11. Malus’ Law
Malus’ law gives the intensity of polarized light after passing through an analyzer:
\[
I = I_0 \cos^2\theta
\]
Where:
\( I_0 \) = intensity of incident polarized light
\( \theta \) = angle between transmission axes
π§ π Summary: Wave Optics at a Glance
Wave optics treats light as a wave phenomenon.
Huygens’ principle explains propagation of wavefronts.
Wavefront is a surface of constant phase.
Interference occurs due to superposition of coherent waves.
Fringe width depends on wavelength, slit separation, and screen distance.
Diffraction causes spreading of light around obstacles.
Central maximum is the brightest in diffraction pattern.
Polarization proves transverse nature of light.
Brewster’s law explains angle of complete polarization.
Malus’ law gives intensity variation of polarized light.
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