Tag: law of malus

Topic tree

1. Huygen’s principle
2. Refraction and reflection of plane waves using Huygen’s principle
3. Coherrent incoherrent addition of waves
4. Interference of light waves by Young’s experiment
5. Diffraction
6. Polarisation

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HUYGEN’S PRINCIPLE

• Huygen’s principle helps to locate the new position and shape of the wavefront at any instant.

• Focus – a fixed point or the centre of the circle
• Locus – moving point of a circle. Locii – a plural form of locus i.e., moving points.
• Wavefront
  • locus of points which oscillate in phase
  • a surface of constant phase
• Spherical waves
  • waves emitted uniformly in all directions
  • the locus of points which have the same amplitude (wave height) and vibrate in same phase
  • have spherical shape

• Plane waves
  • At a larger distance from the source, a small portion of the sphere is considered as a plane. Such waves are called plane waves.

• The Huygen’s principle is basically a geometrical construction.

• A1, A2, A3 represent the spherical wavefront with O as the centre at time, t = 0.
• F1, F2, F3 represent the new spherical wavefront with A1, A2 and A3 as centre and F1, F2 and F3 are in forward positions, but D1, D2 and D3 are backwave, actually they do not exist.

REFRACTION OF A PLANE WAVE

AB = incident wavefront

CD = refracted wavefront

i = incident angle

r = refracted angle

v1 = velocity of light in medium-1 (rarer medium)

v2 = velocity of light in medium-2 (denser medium)

Refraction at a rarer medium

REFLECTION OF A PLANE WAVE BY A PLANE SURFACE

According to law of reflection angle incidence = angle of refraction.

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THE DOPPLER EFFECT

The apparent change in frequency noticed by an observer whent there is a relative motion between the observer and the moving source of light is called Doppler effect.

When there is an increase in wavelength, the Doppler effect is called red shift.

When there is a decrease in wavelength, the Doppler effect is called blue shift.

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THE COHERENT AND INCOHERENT ADDITION OF WAVES

• Interference if one of the properties of light.
• It is based on the superposition principle.
• Superposition at a particular point in the medium is the resultant displacement produced by a number of waves and it is the vector sum of the displacements produced by each of the waves.

When two wave trains superimpose each other they may result either constructive interference resulting bright spot or destrcutive interference resulting dark spot.

Interference of light waves and Young’s double slit experiment

When two sodium lamps illuminate two pinholes S1 and S2, there is no intereference pattern on the screen.

When x and d << D, the denominator S2P + S1P = 2D

For the constructive interference (bright fringes)

The distance between two consecutive dark fringes or bright fringes is called fringe width, w. It is a constant.

DIFFRACTION

DIFFERENCE BETWEEN INTEFERENCE AND DIFFRACTION

INTERFERENCE	DIFFRACTION
1. Superposition of a few secondary wavelets	1. Superposition of large number of secondary waves.
2. Fringes are equally spaced.	2. Wide near the obstacle and becomes narrow towards the shadow region.
3. Result of interaction of two different wavefronts originating from coherent sources.	3. Result of interaction between different parts of the same wavefront.
4. Points of minimum intensity are perfectly dark.	4. Points of minimum intensity are shaded and not perfectly dark.
5. All bright fringes or bands are of uniform intensity.	6. They are not of same intensity.

NOTE:
Energy is conserved in both interference and diffraction by redistributing the light energy by producing dark and bright fringes.

Resolving power of optical instruments

• The ability of the instrument to produce distinctly separate images of two close objects.

• Rayleigh – Two point objects A and B are resolved, when central maximum of diffraction patter of B lies on first secondary minimum of diffraction pattern of A.
• Limit of resolution of an optical instrument – It is the minimum distance between two objects, which can be visible as separate identitites by the optical instruments.

Resolving power of a microscope

• f = focal length of the lens
• 2a = diameter of the lense (Circular aperture)

• A parallel beam of light falls on a convex lens. Because of diffraction effects, the beam gets focused to a spot of radius as given below.

Resolving power depends on the following parameters.

Resolving power of telescope

POLARISATION

• In ordinary light, the vibrations of electric vector take place in all possible direction in a plane perpendicular to the direction of propagation of light.

• Polarisation – the phenomenon of restricting vibrations of light in a particular direction, perpendicular to the direction of wave propagation.
• Nicol or tourmaline crystal acts as a polariser.

Law of Malus

When polarised light is incident on an analyser, the resultant intensity of light (I) transmitted from the analyser is directly proportional to the square of the cosine of the angle between the plane of transmission of analyser and polariser.

Polarisation of light by reflection

The angle of incidence at which the reflected light is completely plane polarised is called the polarising angle (Brewster’s angle).