Light Waves

Light waves are a visible source of energy and a type of wave motion. They have a very short wavelength of 5×10^-4 mm and travel at a speed of 3.0×10⁸ m/s.

Sources of Light Waves

There are natural and artificial sources of light, categorized as luminous and non-luminous.

Natural sources: The sun and stars.
Artificial sources: Candles, electric torches, incandescent and fluorescent lamps.
Luminous objects: Emit light themselves, e.g., the sun, stars, fireflies, and some deep-sea fishes.
Non-luminous objects: Reflect light from luminous objects, e.g., the moon, paper, mirrors, and walls.

Light Rays and Beams

A ray represents the direction of light travel, depicted as a straight line with an arrowhead. A beam is a collection of rays and can be:

Parallel: Rays move in the same direction without intersecting.
Convergent: Rays meet at a point.
Divergent: Rays spread out from a single source.

Rectilinear Propagation of Light

Light travels in a straight line, demonstrated by looking through a straight pipe at a flame. This principle explains:

Eclipses
Shadow formation
Pinhole camera operation

Shadows

Shadows are areas where light is blocked by an opaque object. Types of shadows:

Umbra: Fully dark shadow where light is completely blocked.
Penumbra: Partial shadow where light is partially blocked.

Eclipse

An eclipse occurs when a celestial body casts a shadow on another:

Solar Eclipse: The moon is between the sun and Earth.
Lunar Eclipse: The Earth is between the sun and the moon.

Pinhole Camera

A simple camera consisting of a light-proof box with a small pinhole at one end and a screen at the other. Light from an object passes through the pinhole, forming an inverted image on the screen.

Linear Magnification

Magnification is the ratio of image size to object size:

$$ m = \frac{h_i}{h_o} = \frac{v}{u} $$

Reflection of Plane Mirrors

There are two types of reflection:

Regular Reflection
Diffused Reflection or Irregular Reflection

In regular reflection, parallel rays of light incident on a smooth or polished surface are reflected as parallel rays in one direction.

Laws of Reflection

The incident ray, the reflected ray, and the normal at the point of incidence all lie on the same plane.
The angle of incidence (i) is equal to the angle of reflection (r).

Image Formation by a Plane Mirror

Characteristics of Image Formed by a Plane Mirror

It is the same size as the object.
It is virtual.
It is laterally inverted.
It is upright.
It is as far behind the mirror as the object is in front of the mirror.

Types of Images

Real Image: A real image can be caught on a screen. Light rays actually pass through a real image.
Virtual Image: A virtual image cannot be caught on a screen. It is one through which rays do not actually pass but is visible to the eye.

Lateral Inversion

The effect of a plane mirror on objects placed in front of it, whereby the appearance of the image looks like a reversal of the object, is known as lateral inversion.

Images Formed by Inclined Mirrors

When two mirrors are placed at an angle to each other, the number of images formed is given by:

$$ N = \frac{360°}{θ} - 1 $$

Where:

N = Number of images
θ = Angle of inclination

When θ = 180°, the two mirrors will act as a single mirror and therefore form only one image.

When θ = 0°, the two mirrors are parallel to each other and the image of an object placed between them will be at infinity.

Effect of Mirror Rotation on Reflected Ray - Mirror Galvanometer

If the direction of an incident ray on a mirror is kept constant and the mirror is rotated through an angle, the reflected ray rotates through twice that angle. This fact is utilized in mirror galvanometers (to measure very small electric currents) and in the navigator’s sextant.

Applications of Plane Mirrors

Used in periscopes
Used in kaleidoscopes
Used in sextants

Reflection of Curved Mirrors

Curved mirrors vary in size, shape, and curvature direction. They can be either spherical or parabolic in shape.

Types of Spherical Mirrors

Concave Mirrors: These mirrors are curved inward, resembling the inside of a spoon. They are also known as converging mirrors.
Convex Mirrors: These mirrors bulge outward, resembling the back of a spoon. They are also referred to as diverging mirrors.

Terms Related to Spherical Mirrors

Pole (P): The midpoint of the mirror.
Aperture: The width or diameter of the mirror.
Center of Curvature (C): The center of the sphere from which the mirror is carved.
Radius of Curvature (R): The distance between the center of curvature and the pole.
Principal Axis: An imaginary line passing through the pole and center of curvature.
Principal Focus (F): The point where parallel incident rays converge (concave) or appear to diverge (convex).
Focal Length (f): The distance between the focus and the pole. It is related to the radius of curvature as:
\[ f = \frac{R}{2} \]

Spherical Aberration

Wide-aperture spherical mirrors do not bring all parallel rays to the same focus, leading to spherical aberration. This can be minimized by using small-aperture spherical mirrors or parabolic mirrors in devices like searchlights and car headlights.

Ray Diagram Construction

Rays parallel to the principal axis reflect through the focus.
Rays passing through the center of curvature reflect back along the same path.
Rays passing through the focus reflect parallel to the principal axis.
Rays striking the mirror at the pole obey the law of reflection.

Image Formation by Concave Mirrors

Object beyond C: Image is real, inverted, and diminished, between C and F.
Object at C: Image is real, inverted, and the same size at C.
Object between C and F: Image is real, inverted, and magnified beyond C.
Object at F: Image is at infinity.
Object between F and P: Image is virtual, upright, and magnified behind the mirror.
Object at infinity: Image is real, inverted, and diminished at F.

Image Formation by Convex Mirrors

The image formed by a convex mirror is always virtual, erect, and diminished. It appears between the pole and the principal focus.

Linear Magnification

Defined as the ratio of image height to object height:

\[ m = \frac{h_i}{h_o} = \frac{v}{u} \]

Mirror Formula

The relationship between focal length (f), object distance (u), and image distance (v) is given by:

\[ \frac{1}{u} + \frac{1}{v} = \frac{1}{f} \]

Sign Conventions

Distances measured to the left of the mirror (real) are negative.
Distances measured to the right of the mirror (virtual) are positive.
Real objects and images have positive distances.
Virtual objects and images have negative distances.
Concave mirrors have positive focal lengths, while convex mirrors have negative focal lengths.

Lens

A lens is a portion of a transparent medium bounded by two spherical surfaces or by a plane and a spherical surface.

Types of Lenses

Convex Lens: A convex lens is a converging lens that brings light rays together.
Concave Lens: A concave lens is a diverging lens. There are different types of concave lenses, including:
- Bi-concave
- Plano-concave
- Diverging meniscus

Nature of Images Formed by Convex Lenses

1. Object Beyond 2F

The image is diminished.
The image is formed at the focus (F).
The image is inverted.
The image is real.

2. Object at 2F

The image size is the same as the object.
The image is formed at 2F.
The image is inverted.
The image is real.

3. Object Between F and 2F

The image is magnified.
The image is formed beyond 2F.
The image is inverted.
The image is real.

4. Object at F

The image is formed at infinity.

5. Object Between the Lens and F

The image is magnified.
The image is formed behind the object.
The image is erect.
The image is virtual.

6. Object at Infinity

The image is diminished.
The image is formed at the focus (F).
The image is inverted.
The image is real.

Nature of Images Formed by Concave Lenses

The image is diminished.
The image is formed between the focus (F) and the optical center (C).
The image is erect.
The image is virtual.

Power of a Lens

The power of a lens is the reciprocal of its focal length. It is given by:

\[ P = \frac{1}{F} \]

The unit of power is the dioptre (D), and focal length (F) is measured in meters (m).