14.1 Light

Light: The Dual Nature of Energy

Light is a type of energy that travels in the form of electromagnetic waves. It falls between the ultra-violet and infrared regions in the electromagnetic spectrum, with wavelengths ranging from 3900 Angstroms to 7800 Angstroms.

Wave Nature of Light:

Electromagnetic waves are transverse in nature, meaning light behaves as a transverse wave.

This wave nature explains phenomena like rectilinear propagation (traveling in straight lines), reflection, refraction, interference, diffraction, and polarization of light.

Particle Nature of Light:

However, certain phenomena like the photoelectric effect and Compton effect cannot be explained solely by wave theory.

These phenomena are better explained by the quantum theory of light, proposed by Einstein.

In quantum theory, light is seen as a bundle of energy called a photon, with energy E represented by E = hv, where v is the frequency of the light wave.

Dual Nature of Light:

• Therefore, light exhibits both wave-like and particle-like behavior, known as its dual nature.

Measurement of Speed:

• The speed of light was first accurately measured by Roemer in 1678 AD.
• In vacuum and air, the speed of light is approximately 3 x 10^8 meters per second, representing the maximum speed at which light can travel.

 Refractive Index (R.I.)

Refractive Index (R.I.) is a measure that helps us understand how light behaves when it moves through different materials. It's calculated by comparing the speed of light in a vacuum to the speed of light in a specific material.

• Definition: R.I. is the ratio of the speed of light in a vacuum to the speed of light in the medium.

• Speed of Light: Light travels at different speeds in different materials. In a vacuum, like outer space, light travels at its maximum speed. But when light passes through substances like water or glass, its speed changes.

• Large vs. Small R.I.: A material with a small refractive index means that light travels faster through it. Conversely, a material with a large refractive index means that light travels slower through it.

R.I.=VC​

Where:

• $𝐶$ represents the speed of light in a vacuum (constant value).
• $𝑉$ represents the speed of light in the specific material.

Speed of Light in Different Mediums

Medium	Speed of Light (m/s)
Vacuum	3 x 108
Glass	2 x 108
Water	2.25 x 108
Air	2.04 x 108
Rock Salt	1.96 x 108
Nylon	1.96 x 108

Travel Time of Light

Light, the fastest thing in the universe, takes a certain amount of time to travel from one place to another. Here are some interesting facts about the time it takes for light to reach us from various celestial bodies:

1. Sunlight to Earth: It takes approximately 8 minutes and 19 seconds for light from the Sun to reach the Earth. That means the light you see from the Sun actually left the Sun over 8 minutes ago before reaching your eyes!

2. Moonlight to Earth: The light reflected from the Moon takes a much shorter time to reach the Earth compared to sunlight. It only takes about 1.28 seconds for moonlight to travel from the Moon to the Earth. So when you see the Moon shining in the night sky, you're seeing its light that's only traveled for about 1.28 seconds!

Luminous and Non-luminous Bodies

1. Luminous Bodies: Luminous bodies are objects that emit light by themselves. This means they produce their own light without needing any external source. Examples include the Sun, stars, and electric bulbs. When you see light coming from these objects, it's because they're emitting light on their own.

2. Non-luminous Bodies: Non-luminous bodies are objects that do not emit light by themselves. Instead, they become visible when light from a luminous body falls on them and reflects off their surface. These objects don't produce their own light, but you can still see them because they reflect light from other sources. Examples include the Moon, planets, and everyday objects like tables and chairs.

Classification of Materials by Optical Properties

1. Transparent: Transparent materials are substances that allow most of the incident light to pass through them. This means that light can travel through them easily, and objects on the other side can be seen clearly. Examples include glass and water.

2. Translucent: Translucent materials are substances that allow only a part of the incident light to pass through them. While some light can pass through, it is scattered or diffused, making objects on the other side somewhat visible but not clearly defined. Examples include oiled paper.

3. Opaque: Opaque materials are substances that do not allow any incident light to pass through them. Light is either absorbed or reflected by these materials, and objects on the other side cannot be seen. Examples include mirrors, metals, and wood.

Reflection of Light

When light traveling in one medium encounters the surface of another medium, some of the light is sent back into the original medium. This phenomenon is called the reflection of light.

Laws of Reflection

1. Incident Ray and Reflected Ray: The incident ray, the normal (a line perpendicular to the surface), and the reflected ray all lie in the same plane at the point of incidence on the reflecting surface.

2. Angle of Incidence and Angle of Reflection: The angle at which the incident ray strikes the surface is equal to the angle at which the reflected ray bounces off the surface.

Reflection from a Plane Mirror

1. Virtual and Laterally Inverted Image: The image formed in a plane mirror is virtual, meaning it cannot be projected onto a screen. Also, the image is laterally inverted, meaning left appears as right and vice versa.

2. Size of Image: The size of the image formed in a plane mirror is equal to the size of the object.

3. Distance of Image from Mirror: The distance of the image from the mirror is equal to the distance of the object from the mirror.

4. Motion of Object and Image: If an object moves towards or away from a plane mirror with a speed $𝑣$, the image moves towards or away with a speed of $2𝑣$.

5. Rotation of Mirror: If a plane mirror is rotated by an angle $𝜃$, the reflected ray is rotated by twice that angle, $2𝜃$.

6. Minimum Mirror Size to See Full Image: To see their full image in a plane mirror, a person needs a mirror at least half their height.

7. Number of Images Formed by Inclined Mirrors: The number of images ($𝑛$) formed by two inclined mirrors at an angle $𝜃$ can be calculated based on the formula:

If $\frac{360}{𝜃}$ is an even integer, then $𝑛=\frac{360}{𝜃}-1$.
If $\frac{360}{𝜃}$ is an odd integer and the object is symmetrically placed, then $𝑛=\frac{360}{𝜃}-1$.
If $\frac{360}{𝜃}$ is a fraction, then $𝑛$ is equal to the integral part of $\frac{360}{𝜃}$.

Spherical mirrors come in two types:

1. Concave Mirrors: These curve inward, like the inside of a spoon. They bring light rays together to a point, useful in flashlights, telescopes, and makeup mirrors.

2. Convex Mirrors: They bulge outward, like the outside of a spoon. These mirrors spread out light rays, handy in stores and parking lots for wide-angle views.

Position of Object	Position of Image	Size of Image in Comparison to Object		Nature of Image
		Concave Mirror	Convex Mirror
At infinity	At Focus	Highly diminished	Highly diminished	Real, Inverted
Between infinity and centre of curvature	Between focus and centre of curvature	Diminished	Diminished	Real, Inverted
At centre of curvature	At centre of curvature	Of same size	---	Real, Inverted
Between focus and centre of curvature	Between centre of curvature and infinity	Enlarged	---	Real, Inverted
At focus	At infinity	Highly enlarged	---	Real, Inverted
Between focus and pole	Behind the mirror	Enlarged	---	Virtual, Erect
At infinity	At Focus	Highly diminished	---	Virtual, Erect
In front of mirror	Between pole and focus	Diminished	---	Virtual, Erect

Uses of Concave Mirror:

1. Shaving Glass: It helps people see a magnified reflection for shaving or grooming.
2. Vehicle Reflector: Concave mirrors are used in vehicle headlights and searchlights to reflect light effectively.
3. Ophthalmoscope: Doctors use them to examine the eyes, ears, and nose.
4. Solar Cookers: They concentrate sunlight to cook food efficiently.

Uses of Convex Mirror:

1. Rear View Mirror in Vehicles: They provide a wide field of view behind the vehicle, and the image formed is always upright.
2. Sodium Reflector Lamp: Convex mirrors are used in these lamps to distribute light evenly.