Vardaan Learning Institute

(i) The angle of incidence is equal to the angle of reflection ($\angle i = \angle r$).
(ii) The incident ray, the normal to the mirror at the point of incidence, and the reflected ray, all lie in the same plane.

Characteristics:
1. Image formed is Virtual and Erect.
2. Image size is equal to the object size.
3. Image is formed as far behind the mirror as the object is in front of it.
4. Image is laterally inverted (left appears right and vice versa).

Principal Focus (Concave): A point on the principal axis where light rays parallel to the principal axis actually meet after reflection.
Virtual Focus (Convex): In a convex mirror, parallel rays diverge after reflection. They appear to meet at a point behind the mirror when produced backwards, hence it is called virtual focus.

Snell's Law: The ratio of sine of angle of incidence to the sine of angle of refraction is a constant for the light of a given color and for the given pair of media.
Formula: $\frac{\sin i}{\sin r} = \text{constant} (n)$.
Condition for no bending: When the ray strikes the interface normally (angle of incidence $= 0^\circ$).

1. It always gives an erect (though diminished) image.
2. It has a wider field of view as it is curved outwards, allowing the driver to see a larger area of traffic behind.

Real Image: Formed when light rays actually meet; can be obtained on a screen; usually inverted.
Virtual Image: Formed when light rays appear to meet; cannot be obtained on a screen; usually erect.

Power: The degree of convergence or divergence of light rays achieved by a lens. Reciprocal of focal length (in meters). $P = 1/f(m)$. SI Unit: Diopter (D).
Case 1 ($+50$ cm = $+0.5$ m): $P = 1/0.5 = +2.0$ D. Positive sign indicates Convex Lens.
Case 2 ($-50$ cm = $-0.5$ m): $P = 1/(-0.5) = -2.0$ D. Negative sign indicates Concave Lens.

It provides a wider field of view, allowing shopkeepers to monitor a large part of the shop from a single point.

A rainbow is a natural spectrum appearing in the sky after a rain shower. It is caused by the dispersion of sunlight by tiny water droplets present in the atmosphere.
Three Phenomena: Refraction, Dispersion, and Internal Reflection.
The water droplets act like small prisms. They refract and disperse the incident sunlight, then reflect it internally, and finally refract it again when it comes out of the raindrop.

Stars Twinkle: Stars are distant point-sized sources of light. Their light passes through varying layers of the atmosphere with changing refractive indices. This causes the apparent position of the star to fluctuate slightly and the amount of light entering the eye to flicker, giving a twinkling effect.
Planets Do Not: Planets are much closer and appear as extended sources (collection of points). The fluctuations in light from different points cancel each other out, resulting in zero net variation in brightness.

This is due to Atmospheric Refraction. The air near the ground is denser than higher up. Light from the sun below the horizon travels from rarer to denser layers, bending towards the normal. This makes the sun appear raised above the horizon about 2 minutes before actual sunrise. Same phenomenon occurs at sunset.

Atmospheric Refraction: The refraction of light caused by the earth's atmosphere due to varying optical densities of air layers.
Phenomena: 1. Twinkling of Stars. 2. Advanced sunrise and delayed sunset.

This in due to Scattering of light. The fine particles in the atmosphere scatter blue light (shorter wavelength) more strongly than red light (longer wavelength). The scattered blue light enters our eyes, making the sky appear blue.

Tyndall Effect: The phenomenon of scattering of light by colloidal particles gives rise to the Tyndall effect. This makes the path of the light beam visible.
Example: When sunlight passes through a canopy of a dense forest, tiny water droplets scatter light.

Planets are closer to earth and act as extended sources. The total variation in the amount of light entering our eye from all the individual point sources will average out to zero, nullifying the twinkling effect.

Red is the least scattered colour by fog or smoke because it has the longest wavelength in the visible spectrum. Therefore, it can be seen from a large distance.

Dispersion: The splitting of white light into its component colours (VIBGYOR).
Least Deviation: Red.
Most Deviation: Violet.

Ohm's Law: The potential difference, $V$, across the ends of a given metallic wire in an electric circuit is directly proportional to the current flowing through it, provided its temperature remains the same. ($V = IR$).

Factors: Length ($l$), Area of cross-section ($A$), and Nature of material (Resistivity $\rho$). ($R = \rho l/A$).
(i) Length doubled ($2l$): Resistance becomes double ($2R$).
(ii) Area doubled ($2A$): Resistance becomes half ($R/2$).

1. Alloys have higher resistivity than pure metals, producing more heat.
2. Alloys do not oxidize (burn) easily at high temperatures.

Joule's Law: Heat produced in a resistor is directly proportional to:
1. Square of current ($I^2$) for a given resistance.
2. Resistance ($R$) for a given current.
3. Time ($t$) for which current flows.
($H = I^2Rt$).

1. In series, if one appliance fails, the circuit is broken and none work.
2. Different appliances need different currents to operate properly, which is not possible in series (same current flows).
3. Total resistance increases, reducing the current supply.

Function: It provides a low-resistance path for leakage current to flow to the ground.
Necessity: It ensures that if there is any leakage of current to the metallic body of the appliance, the user does not get a severe electric shock.

Pattern: Concentric circles centered on the wire.
Rule: Right-Hand Thumb Rule. If you hold the 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.

Properties:
1. They emerge from North pole and merge at South pole (outside magnet).
2. Inside the magnet, direction is South to North.
3. They form closed curves.
4. Field is stronger where lines are crowded.
No Intersection: If they did, at the point of intersection there would be two directions of magnetic field, which is impossible for a compass needle to point to simultaneously.