MHT-CET : Physics Entrance Exam

### MHT - CET : Physics - Wave Theory of Light Know More

• Wave Normal and Ray of Light: In an isotropic medium, the light energy propagates in a direction of wave normal. The direction in which the light energy is propagated through a medium is called the direction of the ray of light. Hence, only in an isotropic medium, the direction of the wave normal coincides with the direction of the ray of light.
The difference between isotropic and anisotropic media is that the former has a light velocity that is same for all directions, whereas the latter has a light velocity that depends on the direction of propagation.

• Huygen's Wave Principle: According to Huygen's principle the intensity of the secondary wavelets emitted from the surface of a wave front varies continuously from the maximum in the forward direction to the zero in the forward direction. So it is presumed that the wavelets are effective only in the forward direction. This explains the propagation of the light in the forward direction alone.

• Types of Wave Fronts:
 (i) Spherical Wave Front: A point source of light produces a spherical wave front. In an isotropic medium, a spherical wave front propagates in the form of concentric spherical surfaces. (ii) Cylindrical Wave Front: A line source of light e.g. an illuminated narrow slit, produces a cylindrical wave front. In an isotropic medium, a cylindrical wave front propagates in the form of coaxial cylindrical surfaces. (iii) Plane Wave Front: In an isotropic medium, a small part of the wave surface of a spherical or cylindrical wave front when viewed from a very large distance appears to be plane and is called a plane wave front.
•
• Reflection of Light: When light is incident on the surface of an object, some of the light is returned into the same medium. This phenomenon is called reflection.

(i)

Laws of Reflection: (i) Angle of incidence is equal to the angle of reflection. (ii) The incident ray, the normal and the reflected ray, all lie in the same plane.

(ii)

Deviation of Light on Reflection by a Plane Mirror: Consider a ray of light AO incident at point O on a plane mirror.
Let
Ði = angle of incidence
Ð
r = angle of reflection
ÐAOP = glancing angle

From the fig. shown, we have,
Ði + ÐAOP = Ðr + ÐBOP'
\
ÐAOP= ÐBOP'            …(1)
(...
Ði = Ðr)
Also
ÐAOP = ÐCOP'       …(2)
(Pair of vertically opp.
Ðs)
\ Angle of deviation = ÐCOB = ÐBOP' + ÐCOP' = 2ÐAOP (From (1) and (2))
\ Angle of deviation = 2 ´ glancing angle
\ Angle of deviation of a ray of light by a plane mirror is twice the glancing angle.

 Derivation of reflected ray

(iii)

Rotation of a Mirror: If the direction of the incident ray is unchanged and the plane mirror is rotated by an angle q, in that case, the reflected ray will rotate by angle equal to 2q.

 Rotation of mirror

(iv)

Two Mirrors Inclined with Each Other: When an object is placed in between two parallel mirrors, infinite number of images of the object is formed. If the mirrors are at right angles to each other, the number of images formed is three.

 For mirrors at an angle q, the number of images is N = 360° - 1. q

•
• Refraction of Light: When a ray of light passes obliquely from one transparent medium to another, there is a change in its direction. This change in the direction of a ray of light is called refraction of light.

(i)

Laws of Refraction:

i.                                    When a ray of light is incident on a refracting surface, the ratio of the sine of the angle of incidence to the sine of angle of refraction is a constant for the given pair of media.
The refractive index (
m) for a given pair of media is a constant.

 m = sin i = constant sin r

ii.                                    The above relation is called Snell's Law.

iii.                                    The incident ray, the normal and the refracted ray at the point of incidence all lie in the same plane.

iv.                                    The incident ray and the refracted ray lie on the opposite sides of the normal.

(ii)

Real and Apparent Depth: Consider a point object O placed at the bottom of a transparent medium (water or glass) as shown in the figure. Consider a ray OA which is incident normally on the upper surface. This ray does not bend and travels along AD. Another ray OB, incident very close to OA, is incident at an angle 'i' and is refracted along BC, making an angle 'r' with the normal. Since these two rays are incident very near to each other, the refracted rays AD and BC reach the eye of the observer and appear to diverge from I, which is the virtual image of the point object O.
To an observer, the bottom of the transparent medium appears to be raised to I, and to him the depth appears to be AI, which is known as the apparent depth whereas the real depth is AO.
ÐAOB = i (Pair of alternate angles)
Ð
AIB = r (Pair of corresponding angles)

 Real and apparent depth

 In D AOB, sin i = AB OB

 In D AIB, sin r = AB BI

Since light travels from the given medium to air, the refractive index of air with respect to the medium is given as

 mma = sin i sin r = AB ´ BI OB AB = BI OB

 ... amm = 1 mma = OB BI

Since point B is very close to point A, (i.e. when viewed from vertically above O), then
OB = OA and IB = IA

 \ amm = OA IA

 \ amm = Real Depth Apparent Depth

Apparent Shift: Let real depth OA = t

 Apparent depth IA = t amm

\ Apparent shift OI = OA - IA

 = t - t amm

 \ Apparent shift OI = t 1- t amm

(iii)

Critical Angle: Critical angle is that angle of incidence in the denser medium, for which the angle of refraction in the rarer medium is 90°.

Consider a ray of light travelling from a denser medium to a rarer medium (say air).
When the angle of incidence = critical angle C, the angle of refraction
r = 90°.

 Critical Angle

\ According to Snell's law, the refractive index of air with respect to the medium is given by

 mma = sin C sin 90° = sin C

 ... amm = 1 mma

 \ amm = 1 sin C

E.g. The critical angle of ordinary glass is nearly 42°.

(iv)

Total Internal Reflection: When the critical angle is exceeded, the incident ray of light is reflected into the same medium (denser medium). This phenomenon is known as total internal reflection.
Total internal reflection takes place at the surface separating an optically denser medium from an optically rarer medium when light passes from the denser medium to the rarer medium and the angle of incidence exceeds the critical angle C. The surface separating the denser medium and the rarer medium acts as a perfect mirror under the condition of total internal reflection.

 Critical Angle and Total Internal Reflection

Effects of Total Internal Reflection:

i.

Sparkle or brilliance of a diamond: Diamond has a very high refractive index about 2.4, hence its critical angle is very small, nearly 24°. Light entering the cut face of the crystal suffers repeated total internal reflection within the crystal. It is this light energy that remains trapped within the crystal that accounts for the brilliance or sparkle of the diamond.

 Brilliance of diamond

ii.

Mirage: It is an optical illusion which is due to total internal reflection. It is created due to refraction in the different layers of air due to their different densities. This illusion which is generally experienced on a hot, sunny day, gives the impression that there is a pool of water ahead at some distance from the observer.

 Mirage

iii.

Optical Fibre: An optical fibre is a transparent fibre used to conduct light through the phenomenon of total internal reflection.

iv.

Cracks in a glass window pane appears silvery.

v.

An empty test tube held obliquely in water and observed from above appears silvery.

•
• Dual Nature of Light

i.            Light energy is supposed to exhibit dual nature, i.e. it sometimes behaves as waves and sometimes as particles.

ii.            When we are dealing with phenomena, which involve a statistical array of microscopic events, the wave concept must be used. The phenomena like interference, diffraction, polarisation, etc. could only be explained if light energy was supposed to consist of waves.

iii.            On the other hand, when we are dealing with a single microscopic event, the particle nature, or the photon concept must be used. The phenomena like photoelectric effect, electron emission etc. could only be explained if light energy was supposed to consist of packets of energy called photons which behaved like particles and travelled through space with the speed of light.

• Colours of Objects: The colour of an object depends on the wavelength of light falling on it. When white light is incident on an object, a part of the light is absorbed. The part of light that is reflected imparts that colour to the object.
A red object absorbs all other colours of white light and reflects red. Hence the object appears red in colour. However, if the same object is viewed in blue or green light, these colours are absorbed. But since the object is capable of reflecting only the red component, it reflects nothing. Hence the object appears black in blue or green light.
 When viewed in white light When viewed in blue light

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