### Characteristics of light :

- Intensity (Power per unit solid angle)
- Wavelength (Color)
- Spectral width ( purity of color)
- Polarization

Circular

Elliptical

#### The characteristics of light are summarized in the following.

- The first three parameters scalar characteristics of light where as the last parameter, polarization, describes the vector nature of light.
- The choice of wavelength depends upon the loss profile of the medium. For optical fiber the wavelength has to be 1300nm or 1550nm for low loss.
- The spectral width has direct bearing on the data rate which the medium can support. Larger the spectral width, smaller is the data rate. A semiconductor laser typically has spectral width about 20 to 100 times less compared to LED. Consequently, laser based communication can support much higher data rates.
- Polarization in a intrinsic property of an electromagnetic wave.
- Light is an Electromagnetic wave.
- It consists wave fronts. The lines normal to the wave fronts are called the light rays.
- If the phase fronts are concentric spheres, the light is called a spherical wave, and if the phase fronts are parallel planes, the light is called a plane wave.
- For a plane waves the rays are parallel whereas for the spherical wave, the emerge from the center of the spheres.
- If the source is a a finite distance, the appropriate model is the spherical wave model, and if the source is assumed to be at infinite distance, the plane wave model is appropriate.
- A plane wave can be represented by a wave function which is a composite function of space and time

### Wave Function

: Amplitude of the wave

: Angular frequency of the wave (rad/s)

: Phase constant (rad/m)

: Distance

: Time

### Vector nature of light

The vector nature of light is described using two types of vectors: electric field vector and magnetic field vector. These vectors are perpendicular to each other and to the direction of propagation of the light wave. The electric field vector is denoted by E, and the magnetic field vector is denoted by B.The relationship between these two vectors is given by Maxwell's equations. These equations describe the behavior of electromagnetic waves, which include light waves. The equations show that the electric and magnetic fields are coupled, which means that a change in one field will induce a change in the other field.

The magnitude of the electric and magnetic fields varies with time and position. This variation is described using sinusoidal functions. The electric field is given by:

E = E0sin(kx - Ï‰t)

where E0 is the amplitude of the electric field, k is the wave vector, x is the position, Ï‰ is the angular frequency, and t is time.

The magnetic field is given by:

B = B0sin(kx - Ï‰t)

where B0 is the amplitude of the magnetic field.

The wave vector, k, represents the direction and wavelength of the wave. The angular frequency, Ï‰, is related to the wavelength by the equation:

Ï‰ = 2Ï€c/Î»

where c is the speed of light and Î» is the wavelength.

### Propagation of light

Propagation of light refers to the way in which light travels through space or matter.#### Laws of Light Propagation:

#### Law of Reflection:

The law of reflection states that when a light ray strikes a surface, the angle of incidence is equal to the angle of reflection, where both angles are measured with respect to the normal line, which is a line perpendicular to the surface. This law is applicable to all types of surfaces, whether they are smooth or rough. The law of reflection is given by the formula:

Î¦1= Î¦2

where Î¦1 is the angle of incidence, and Î¦2 is the angle of reflection.

Î¦1= Î¦2

where Î¦1 is the angle of incidence, and Î¦2 is the angle of reflection.

#### Law of Refraction:

The law of refraction, also known as Snell's law, states that when a light ray passes from one medium to another, it changes direction, and the angle of refraction is related to the angle of incidence and the refractive indices of the two media. The law of refraction is given by the formula:

n1 sin(Î¸1) = n2 sin(Î¸2)

where n1 and n2 are the refractive indices of the two media, Î¸1 is the angle of incidence, and Î¸2 is the angle of refraction.

n1 sin(Î¸1) = n2 sin(Î¸2)

where n1 and n2 are the refractive indices of the two media, Î¸1 is the angle of incidence, and Î¸2 is the angle of refraction.

#### Refractive Index :

The amount of refraction or bending that occurs at the interface of two
materials of different densities is usually expressed as refractive index of
two materials. Refractive index is also known as index of refraction and is
denoted by n.

Based on material density, the refractive index is expressed as the ratio of
the velocity of light in free space to the velocity of light of the dielectric
material (substance).

The refractive index for vacuum and air is 1.0 for water it is 1.3 and for glass
refractive index is 1.5.

#### Total Internal Reflection

When a light ray passes from a medium with a higher refractive index to a medium with a lower refractive index, the angle of refraction may be greater than 90 degrees. In this case, total internal reflection occurs, and the light ray is reflected back into the original medium. The critical angle is the angle of incidence at which the angle of refraction is 90 degrees, and any incident angle greater than the critical angle will result in total internal reflection. The critical angle is given by the formula:Î¸c = sin⁻¹(n2/n1)

where n1 and n2 are the refractive indices of the two media.

#### Formulas for Light Propagation:

Speed of Light: The speed of light in a vacuum is a constant value, denoted by the letter "c". Its value is approximately 299,792,458 meters per second. The speed of light in a medium with a refractive index n is given by the formula v = c/n, where v is the speed of light in the medium.#### Diffraction

Diffraction is the bending of light around an obstacle or through an opening. The amount of diffraction depends on the wavelength of the light and the size of the obstacle or opening. The diffraction pattern is characterized by bright and dark fringes that result from the interference of the diffracted waves. The diffraction angle is given by the formula:sin(Î¸) = nÎ»/d

where Î¸ is the diffraction angle, n is the order of the diffraction pattern, Î» is the wavelength of the light, and d is the size of the opening or obstacle.

#### Snell's Law:

Snell’s law states how light ray reacts when it meets the interface of
two media having different indexes of refraction.

Let the two medias have refractive indexes n1 and n2 where n1 >n2. Î¦1 and Î¦2 be the angles of incidence and angle of refraction respectively.
Then according to Snell’s law, a relationship exists between the refractive index of both
materials given by
n1 sinÎ¦1 = n2 sinÎ¦2

The refracted wave will be towards the normal when n1 < n2 and will
away from it when n1 > n2.

#### Critical Angle:

The critical angle is the angle of incidence at which the angle of refraction is 90 degrees. It is given by the formula Î¸c = sin⁻¹(n2/n1), where n1 and n2 are the refractive indices of the two media.

#### Ray Model:

In the ray model, light is treated as a collection of straight lines or rays that travel in a straight line until they interact with an object or a medium. The ray model is useful for understanding the behavior of light when it interacts with simple objects, such as mirrors and lenses, and for predicting the path of light in optical systems. The ray model assumes that light travels in straight lines, and that the direction of the ray can be changed by reflection or refraction at an interface between two media. The angle of reflection is equal to the angle of incidence, and the angle of refraction is given by Snell's law.#### Wave Model:

In the wave model, light is considered as a wave-like phenomenon that exhibits interference, diffraction, and polarization. The wave model is useful for understanding the behavior of light when it interacts with complex objects, such as gratings and diffraction slits, and for describing the phenomenon of interference. In the wave model, light is characterized by its wavelength, frequency, and amplitude. Light waves can interfere constructively or destructively, depending on the phase difference between the waves. Diffraction occurs when a wave interacts with an object or an aperture, and the wave is diffracted into different directions. Polarization is a property of light waves that describes the orientation of the electric field vector.#### Comparison:

The ray model and the wave model are both useful for understanding the behavior of light, but they are based on different assumptions and are useful in different situations. The ray model is a simplified approach that is useful for understanding the behavior of light when it interacts with simple objects and for predicting the path of light in optical systems. The wave model is a more complex approach that is useful for understanding the behavior of light when it interacts with complex objects and for describing the phenomenon of interference. In general, the ray model is more useful for designing and optimizing optical systems, while the wave model is more useful for understanding the fundamental nature of light.**Q1. A light ray is incident from medium-1 to medium-2. If the refractive indices of medium-1 and medium-2 are 1.5 and 1.36 respectively then determine the angle of refraction for an angle of incidence of 30 degree.**

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