Physics Master Notes (2025-26)

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UNIT 1: LIGHT – REFLECTION & REFRACTION

1. Reflection of Light

            Laws of Reflection:
            Angle of Incidence = Angle of Reflection (∠i = ∠r).
The Incident ray, the Reflected ray, and the Normal all lie in the same plane.

        

2. Spherical Mirrors (Concave & Convex)

Uses (Most Asked):
1. Concave: Shaving mirrors (enlarged image), Torches/Headlights (parallel beam), Solar furnaces (concentrate heat), Dentists.
2. Convex: Rear-view mirrors (Wider field of view + Always erect image).

A. Key Terms (Mirrors & Lenses)

Pole (P) / Optical Centre (O): The geometric center of the spherical mirror/lens.
Centre of Curvature (C): The center of the hollow glass sphere of which the mirror/lens is a part.
Principal Axis: The straight line passing through the Pole (P) and Center of Curvature (C).
Principal Focus (F): The point on the principal axis where light rays parallel to the axis converge (Concave Mirror/Convex Lens) or appear to diverge from (Convex Mirror/Concave Lens).
Focal Length (f): The distance between the Pole (P) and the Principal Focus (F).
Aperture: The diameter of the reflecting surface or the lens.

Figure 1.0: Key Terms - Concave Mirror (Left) & Convex Lens (Right)

Relation: Radius of Curvature (R) = 2 × Focal Length (f)

B. Rules for Image Formation (Mirrors)

            Rule 1: A ray parallel to Principal Axis passes through Focus (F) after reflection.
                
Rule 2: A ray passing through Focus (F) becomes parallel to Principal Axis.
Rule 3: A ray passing through Center of Curvature (C) retraces its path.
Rule 4: A ray incident obliquely at the Pole (P) reflects with equal angle (∠i
                    = ∠r).

        

Figure 1.0b: Rules for Ray Tracing (Mirrors)

C. Image Formation by Spherical Mirrors & Lenses

Figure 1.1: Ray Diagrams for Concave Mirror

Image formation by concave mirror
Object Position	Image Position	Size	Nature
At Infinity	At Focus F	Highly Diminished	Real & Inverted
Beyond C	Between F and C	Diminished	Real & Inverted
At C	At C	Same Size	Real & Inverted
Between C and F	Beyond C	Enlarged	Real & Inverted
At F	At Infinity	Highly Enlarged	Real & Inverted
Between P and F	Behind the Mirror	Enlarged	Virtual & Erect

Figure 1.2: Ray Diagrams for Convex Mirror

Image formation by convex mirror
Object Position	Image Position	Size	Nature
At Infinity	At Focus F (Behind)	Highly Diminished	Virtual & Erect
Between Infinity & Pole	Between P and F (Behind)	Diminished	Virtual & Erect

3. Mirror Formula & Magnification

Mirror Formula:
1v + 1u = 1f

Magnification (m):
m = h'h = - vu

Sign Convention Hack:

u (Object dist): ALWAYS Negative (-).
f (Focal Length): Concave = (-); Convex = (+).
m (Magnification): (-) = Real/Inverted; (+) = Virtual/Erect.

4. Refraction of Light

$Refraction Rules$ Figure 1.3: Refraction Rules

Snell's Law: sin isin r = constant (n)

Absolute Refractive Index (n_m): n_m = c (Speed in air)v (Speed in medium)

$Refraction through Glass Slab$ Figure 1.4: Refraction through Glass Slab

5. Lenses: Diagrams & Formulas

A. Rules for Image Formation (Lenses)

            Rule 1: A ray parallel to Principal Axis passes through Principal Focus (F).
Rule 2: A ray passing through the Optical Centre (O) goes
                    undeviated (straight).
                
Rule 3: A ray passing through Principal Focus (F) becomes parallel to Principal
                    Axis.

        

Figure 1.5a: Rules for Ray Tracing (Lenses)

B. Ray Diagrams Checklist

Figure 1.5b: Ray Diagrams for Convex Lens

Image formation by convex lens
Object Position	Image Position	Size	Nature
At Infinity	At Focus F₂	Highly Diminished	Real & Inverted
Beyond 2F₁	Between F₂ and 2F₂	Diminished	Real & Inverted
At 2F₁	At 2F₂	Same Size	Real & Inverted
Between F₁ and 2F₁	Beyond 2F₂	Enlarged	Real & Inverted
At Focus F₁	At Infinity	Highly Enlarged	Real & Inverted
Between F₁ and O	On same side as object	Enlarged	Virtual & Erect

Figure 1.6: Ray Diagrams for Concave Lens

Image formation by concave lens
Object Position	Image Position	Size	Nature
At Infinity	At Focus F₁	Highly Diminished	Virtual & Erect
Between Infinity & O	Between F₁ and O	Diminished	Virtual & Erect

Lens Formula: 1v - 1u = 1f

Magnification (Lens): m = vu (Note: Positive sign)

Power (P): P = 1f (in Meters!) (Unit: Dioptre D)

UNIT 2: HUMAN EYE & COLOURFUL WORLD

1. Structure of the Eye

Part	Function
Cornea	Front bulging part. Most refraction happens here.
Iris	Controls pupil size (Dark muscular diaphragm).
Pupil	Regulates amount of light entering.
Ciliary Muscles	Adjusts lens curvature (Power of Accommodation).
Retina	Screen with light-sensitive cells.

Figure 2.0: Structure of the Human Eye

2. Defects of Vision (Quick Theory Table)

Defect	Definition & Image Position	Causes	Correction
Myopia (Near-sightedness)	Can see near objects clearly; distant objects blurry. Image forms in front of retina.	1. Excessive curvature of eye lens. 2. Elongation of eyeball.	Concave Lens
Hypermetropia (Far-sightedness)	Can see distant objects clearly; near objects blurry. Image forms behind the retina.	1. Focal length of eye lens is too long. 2. Eyeball is too small.	Convex Lens
Presbyopia (Old age Hypermetropia)	Power of accommodation decreases with ageing. Near point recedes.	1. Weakening of ciliary muscles. 2. Diminishing flexibility of lens.	Bi-focal Lens (Concave top, Convex bottom)

Figure 2.1: Myopia (Defect and Correction)

Figure 2.2: Hypermetropia (Defect and Correction)

3. Prism & Light Phenomena

Figure 2.3: Dispersion of White Light by Glass Prism

Figure 2.4: Recombination of Spectrum

Rainbow Formation (From NCERT)

A rainbow is a natural spectrum appearing in the sky after a rain shower. It is caused by dispersion of sunlight by tiny water droplets, present in the atmosphere. A rainbow is always formed in a direction opposite to that of the Sun.

Mechanism: The water droplets act like small prisms.
3-Step Process:
1. They refract and disperse the incident sunlight.
2. Then they reflect it internally (Internal Reflection).
3. Finally, they refract it again when it comes out of the raindrop.

Figure 2.5: Rainbow Formation

4. Atmospheric Refraction

Definition: Refraction of light caused by different layers of the atmosphere having varying optical densities (hot air is rarer, cold air is denser).

            Twinkling of Stars:
                    
• Stars are distant point-sized sources of light.
                    
• As starlight enters the atmosphere, it undergoes refraction continuously due to changing air
                    density.
                    
• The apparent position of the star fluctuates, and the amount of light entering the eye
                    flickers.
                
Why Planets Don't Twinkle:
                    
• Planets are closer and appear as extended sources (collection of many point
                    sources).
                    
• Changes in light from different points cancel each other out. Net variation is zero.
                
Advanced Sunrise & Delayed Sunset:
                    
• The Sun is visible 2 minutes before actual sunrise and 2 minutes
                        after actual sunset.
                    
• Reason: Light bends near the horizon due to atmospheric refraction, making
                    the Sun appear higher than it effectively is.

$Atmospheric Refraction Phenomena$ Figure 2.6: Atmospheric Refraction Phenomena

5. Scattering of Light

            Tyndall Effect: The phenomenon of scattering of light by colloidal particles (e.g.,
                    sunlight passing through a dense forest canopy or smoke-filled room). The path of the beam becomes
                    visible.
Why Sky is Blue:
                    
• Air molecules and fine particles are smaller than the wavelength of visible light.
                    
• They scatter shorter wavelengths (Blue/Violet) more strongly than long
                    wavelengths (Red).
                    
• The scattered blue light enters our eyes. (Note: We see blue instead of violet because our
                    eyes are more sensitive to blue).
                

        

Natural Phenomena Reasoning Summary:
1. Stars Twinkle: Point source + Changing atmospheric density.
2. Planets Don't Twinkle: Extended source + Variations cancel out.
3. Blue Sky: Scattering of blue light by fine air particles.
4. Danger Signals Red: Red has longest Wavelength (λ), scattered least by fog/smoke.

UNIT 3: ELECTRICITY

1. Basics & Definitions

            Electric Current (I): Rate of flow of charge. I = Q/t. 

                    1 Ampere: Flow of 1 Coulomb charge per 1
                    Second.
                
Potential Difference (V): Work done to move unit charge. V = W/Q. 

                    1 Volt: 1 Joule work done to move 1
                    Coulomb charge.
                
Charge on 1 Electron (e): 1.6 × 10-19 C.

2. Circuit Diagram Symbols

Figure 3.1: Standard Circuit Symbols

3. Ohm's Law & Resistance

A. Verification of Ohm's Law (Experiment)

Figure 3.2: Circuit for Ohm's Law

            Aim: To verify V ∝ I for a resistor.
Setup: Connect Resistor, Ammeter (Series), Voltmeter (Parallel), Battery, and
                    Rheostat.
Procedure: Vary current using Rheostat. Note V and I readings. Calculate V/I ratio
                    (It remains constant).
Observation: V-I Graph is a straight line passing through origin.

        

B. Graphs (V-I vs I-V)

Figure 3.3: V-I Graph for Ohmic Conductor

Important Note on Graphs:
• V-I Graph: Slope = Resistance (R).
• I-V Graph: Slope = 1/Resistance (1/R). (No image required, just remember this relation).

V = IR (at const. Temp)

Resistance Factors: R = ρ LA

1. Directly proportional to Length (L).
2. Inversely proportional to Area (A).
3. Depends on Nature of Material (ρ) & Temperature.

Conceptual Trap:
If wire is stretched to double length:
Length becomes 2L, Area becomes A/2.
New Resistance R' = 4 times the original R.

4. Series vs Parallel

Series	Parallel
Current (I) same.	Voltage (V) same.
R_eq = R₁ + R₂	1/R_eq = 1/R₁ + 1/R₂

Figure 3.4: Series and Parallel Circuits

5. Heating Effect & Power (Expanded)

A. Joule's Law of Heating

Heat produced in a resistor is:

            Directly proportional to square of current (H ∝ I2).
Directly proportional to resistance (H ∝ R).
Directly proportional to time (H ∝ t).

        

H = I²Rt (Heat in Joules)

B. Electric Power

Rate at which electric energy is consumed.

Power Formulas:
P = VI = I²R = V²/R

Commercial Unit of Energy:
1 kWh (1 Unit) = 3.6 × 10⁶ Joules

C. Practical Applications (Exam Favorite)

            Electric Bulb: Filament made of Tungsten because:
                    
1. Very high melting point (3380°C).
                    
2. Does not oxidize (burn) easily at high temp.
                
Electric Fuse: Safety device made of Lead-Tin Alloy.
                    
• Has appropriate melting point. Breaks circuit if Current > Safe Limit.
                    
• Always connected in Series with Live wire.
                
Heating Elements (Iron, Toaster): Made of Nichrome (Alloy).
                    
• High Resistivity & High Melting Point.
                    
• Does not oxidize easily red hot.
                    
• Its resistance increases slightly with temperature.

UNIT 4: MAGNETIC EFFECTS

1. Magnetic Field Patterns (Crucial Diagrams)

Figure 4.1: Magnetic Field due to Straight Wire & Circular Loop

2. Right-Hand Thumb Rule (Exam Definition)

What to write in Exam:
Imagine you are holding a current-carrying straight conductor in your right hand such that the thumb points towards the direction of current. Then your fingers will wrap around the conductor in the direction of the field lines of the magnetic field.

Figure 4.2: Right-Hand Thumb Rule

3. Solenoid & Bar Magnet Behavior

Figure 4.3: Magnetic Field Lines: Solenoid vs Bar Magnet

4. Electromagnet vs Permanent Magnet

Electromagnet (Temporary)	Permanent Magnet

Created by current in solenoid with soft iron core.	Natural or made of steel/alloys (Alnico).
Strength can be changed.	Strength is fixed.
Polarity can be reversed.	Polarity cannot be reversed.

5. Force on Conductor & Fleming's Left Hand Rule

A current-carrying conductor placed in a magnetic field experiences a force (Motor Principle).

Fleming's Left Hand Rule (Exam Definition):
Stretch the thumb, forefinger and middle finger of your left hand such that they are mutually perpendicular.
• Forefinger: Points in the direction of Magnetic Field.
• Middle finger: Points in the direction of Current.
• Thumb: Points in the direction of Motion (Force).

Figure 4.4: Force on Current-Carrying Conductor in Magnetic Field

6. Domestic Circuits

Wire	New Color	Function
Live	Brown	Carries current (220V)
Neutral	Blue	Return path (0V)
Earth	Green/Yellow	Safety (Leakage current)

AC vs DC (Must Know):
1. AC (Alternating Current): Direction reverses periodically (50 Hz).
2. DC (Direct Current): Unidirectional (Battery).

Figure 4.5: Domestic Electric Circuit