Light wave and Optics wave Assignment Help




Light or visible light is the portion of electromagnetic radiation that is visible to the human eye, responsible for the sense of sight. Visible light has a wavelength in a range from about 380 or 400 nanometres to about 760 or 780 nm, with a frequency range of about 405 THz to 790 THz. In physics, the term light often comprises the adjacent radiation regions of infrared (at lower frequencies) and ultraviolet (at higher), not visible to the human eye.

Primary properties of light are intensity, propagation direction, frequency or wavelength spectrum, and polarization, while its speed, about 300,000,000 meters per second (300,000 kilometers per second) in vacuum, is one of the fundamental constants of nature.

Light, which is emitted and absorbed in tiny "packets" called photons, exhibits properties of both waves and particles. This property is referred to as the wave–particle duality. The study of light, known as optics, is an important research area in modern physics.

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Wave Optics

Ray Optics and Optical Instruments

Wave Optics Wavefront.

(a) A wavefront is the locus of all the points in space which receive light waves from a source in phase. If the source of light is a point source and the medium is homogeneous and isotropic, the wavefront will be spherical in shape. However, at very large distance from the point source, the shape of the wavefront changes from spherical to a plane wavefront.

(b) Shape of the wavefront may also change due to its passage through a refracting medium such as a lens.

(c) A wavefront is always normal to the light rays.

(d) A wavefront does not propagate in the backward direction.

Cylindrical wavefront. When the source of light is linear in shape, cylindrical wavefront is formed.

Plane wavefront. A small part of a spherical or cylindrical wavefront originating from a distant source

can be considered as a plane   wavefront

 

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Huygens' Principle.

(i) Each point on a given primary wavefront acts as a source of secondary wavelets, sen

ding out disturbances (waves) in all directions in a similar manner as the original source of light does.

(ii) The new position of the wavefront at any instant (secondary wavefront) is given by the forward envelope to the secondary wavelets at that instant. Huygens' construction (See Fig.)

Reflection on the Basis of Wave Theory.

The angle between the reflected ray and the normal is called angle of reflection.

The two laws of reflection are : (0 Angle of incidence is equal to angle of reflection.

(ii) The incident ray, the reflected ray and the normal at the point of incidence all lie in the same plane. Proof using Huygens' Principle. Consider a plane wave AB incident at an angle i on a reflecting surface MN. If v is the speed of the wave in the medium and t is the time taken by the wavefront to cover the distance BC, then BC = vt

To construct the reflected wavefront we draw an arc (representing reflected wavefront) of radius vt from the point A. Draw a tangent on the arc (i.e., reflected wavefront). We obtain AE - BC = v t

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From the triangles ECA and BAC we will find that they are congruent. This is the law of reflection. Thus Zi=Zr

Refraction on the Basis of Wave Theory

 The phenomenon of change in the path of light as it travels from one medium to another is called refraction. Its two laws are : (0 The incident ray, the normal to the refracting surface at the point of incidence and the refracted ray all lie in the same plane.

(ii) For a given pair of media and for light of a given wavelength, the ratio of the sine of the angle of incidence to the sine of the angle of refraction is constant. Hence, laws of refraction are established on the basis of wave theory.

Proof using Huy gens' Principle. We will now use Huy gens' principle to derive the laws of refraction. Let PP' represent the surface separating medium 1 and medium 2. Let Vj and v2 represent the speed of light in medium 1 and medium 2 respectively. Take a

We draw an arc (representing refracted wavefront) of radius v2t from the point A in the second medium. Draw a tangent on this arc. . CE gives refracted wavefront. From the triangles ABC and AEC we obtain

• • BC V m

sin i =-= —— ...(1)

AC AC

a ■ AE V ™ and sin r =-=---..(2)

AC AC

where i and r are the angles of incidence and refraction respectively. Thus

sin* = VL (3)

sin r v2

Now, if c represents the speed of light in vacuum, then,

b, = - ...(4)

V1

c

andn. -— ...(5)

2 v2

In terms of the refractive indices, equation 3 can be written as sin i = n2 sin r This is the Snell's law of refraction

Behaviour of a Prism, Lens and Concave Mirror Towards a Plane Wavefront.

Prism bends an incident wavefront towards its base after it passes through the prism.

Convex lens. When a plane wavefront passes through a convex lens it gets converted into a converging spherical wavefront.

Concave mirror. After reflection from a concave mirror plane wavefront turns into a converging spherical wavefront.

Visible light waves:

The visible light waves are the electromagnetic waves. The visible light waves produce by the accelerating charge particle. As the charge particle is accelerated, it produces electric and magnetic fields, which are changing in nature, and they produce electromagnetic waves. There is a wide range of electromagnetic waves out of which one part is called as visible light waves.

Visible Light Waves:

The visible light is in the very narrow region of electromagnetic spectrum. The visible light waves can be detected by human eye. The frequency of visible light waves is ranging from 4 × 1014 Hertz to 8 × 1014 Hertz. The wavelength range of visible light waves lies between 400 nanometer to 700 nanometer. The visible light waves consists of seven colored light such as violet, indigo, blue, green, yellow, orange, red. The visible light waves are produced by atomic excitation. The visible light waves emitted or reflected from objects around us provide the information about the world surrounding us.

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Characteristics of Visible Light Waves:

The characteristics of visible light waves are given below:

(i) The visible light waves are produced by accelerating or oscillating charged particles.

(ii) The visible light waves do not require any material medium for their propagation.

(iii) The visible light waves are transverse in nature.

(iv) The visible light waves travel in free space with a speed of 3 × 108 metre per second.

(v) In visible waves the sinusoidal variation in both electric and magnetic fields vectors occurs simultaneously.

(vi) The direction of electric and magnetic fields variations are perpendicular to each other.

(vii) The velocity of visible light waves depends entirely on the electric and magnetic properties of the medium in which they travel and is independent of the amplitudes of the field vectors.

(viii) The velocity of visible light waves in any dielectric medium is less than 3 × 108 metre per second.

(ix) The visible light wave carry energy, which is, divided equally between electric field and magnetic field vectors.

(x) The electric field vector is responsible for the optical effects of an electromagnetic wave and it is called as light vector or optic vector.

Light Geometric Optics

Light is a form of energy that produces the sensation of vision. Light itself invisible. When it falls on an object the scattered light enters the eye and the object becomes visible. In this process the light undergoes modifications exhibiting its properties. Optics is the study of these interactive properties of light. The path along which light energy travels is called a ray. In a homogeneous medium a ray may be represented by a straight line with an arrow head in the direction in which the energy travels. The study of light based on the concept of rays with the help of geometrical principles is called Geometrical Optics.

Laws of Geometric Optics for Light

 Geometrical optics is based on three general laws .  (1) The law of rectilinear propagation of light. (2) The laws of reflection . (3) The laws of refraction.
Law of rectilinear propagation of light  :  In a homogeneous medium light travels along a straight line.
Reflection and Refraction : When light travelling in a medium is incident on a surface separating the medium from another medium it will undergo the following changes:
(I)  a part of the light comes back into the same medium from the surface in a definite direction. This part of the light is called reflected part and this phenomenon is called reflection.
(ii) Another part of the light enters the second medium at the surface which is the refracted part and the phenomenon is called refraction.
Types of Reflection
1) When the separating surface is plane, a parallel beam of light incident on it will remain parallel even after reflection as shown in the figure below. This type of reflection is said to be regular. Reflection from a plane mirror is an example of this type.
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2) If the separating surface is uneven, the normal at different points will be in different directions. But the incident rays of light at different points obey the laws of reflection. So, the rays that were parallel before reflection will be reflected in random directions as shown ind the second figure above. This kind of reflection is called diffuse reflection. We can see an object due to diffuse reflection of light by the object.
        
                                     

Light Geometric Optics : Refraction

  Refraction of light is the bending of light when it travels from one medium to another medium. The various phenomena that occur when light travels from one medium to another medium.  If the second  medium is denser with respect to the first, then according to Snell , sin(i) / sin(r)  = v1 / v2 . Where i , r are the angles of incident and refracted rays, v1 , v2 are the velocities of light in the two media.

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