here brewster angle formula for perpendicular polarization derivation , what is brewster angle class 12 ?
Some Important Points about Interference of Light
1. In Young’s double slit experiment, if monochromatic light is replaced by white light then central fringe will be white; all other fringes will be coloured. White light consists of colours between violet and rad (VIBGYOR). Wavelength λ is the shortest for violet light and longest for red light. At the central fringe, the path difference for all colours is zero. Hence at the central fringe, all colours superpose to give a white fringe. The first bright fringe after the central fringe will be violet colour. 2. In Young’s double slit experiment, if one of the slits is covered with a transparent film or sheet of thickness t and refractive index µ, then
(a) the path difference at the centre of the screen will not be zero, it will be equal to (µ – 1)t.
(b) the entire fringe pattern will shift by an amount
(c) at the centre of the screen there will be a bright fringe if (µ – 1) t = nλ; n = 1, 2, 3, … etc.
(d) at the centre of the screen there will be a dark fringe if
(e) the fringe width will remain the same.
(f) the intensity of light from the covered slit will decrease due to absorption by the film or sheet. Hence intensity of bright fringes will decrease and dark fringes will have some finite intensity (because the two interfering beam do not now have equal intensity). Hence the fringe pattern will become less distinct.
3. If one of the slits in Young’s double slit experiment is closed (or covered with black paper), the interference pattern is replaced by single slit diffraction pattern which has a bright central fringe bordered on both sides by fringes of decreasing intensity.
4. If Young’s interference experiment is performed in still water rather than in air, the fringe width will decrease. Since the refractive index of water is greater than that of the air, the speed of light in water (v) will be less than that in air (c). Since the frequency of light is the same in all media, λw = v/v and
Now μw = 4/3. Hence λw < λa . Fringe width β ∝ λ. Hence β in water < β in air.
5. In Young’s interference experiment, if the beam of light has two wavelengths λ1 and λ2, their maxima will coincide if n1 λ1 = n2 λ2 , where n1 and n2 are integers.
6. In an interference experiment if the two coherent light sources have intensities in the ratio n : 1, i.e. I1/I2 = n, then the ratio of the intensity of maxima and minima in the interference pattern is
7. In an interference experiment with two coherent light sources, if the ratio of the intensities of maxima and minima in the interference pattern is n : 1, i.e. Imax/Imin = n , then ratio of the intensities of the coherent sources is
8. In an interference experiment, if the two coherent sources have intensities in the ratio n : 1, then in the interference pattern
9. The intensity of light emerging from a slit is proportional to its width. If the two slits in Young’s interference experiment have widths in the ratio
10. In Young’s double slit experiment , if x is the width of the source slit S and X its distance from the plane of the slits, the interference fringes will not be seen (because the interference pattern becomes indistinct) if the condition
is not satisfied.
9. Resolving Power Resolving power of an optical instrument is its ability to produce distinctly separate images of two objects very close together.
(a) Resolving power of a microscope
where 2θ = angle of the cone of light rays entering the objective of the microscope , µ = refractive index of the medium between the object and the objective and λ = wavelength of light used to illuminate the object
(b) Resolving power of a telescope
where D = diameter of objective and λ = wavelength of light
10. Polarization of Light The phenomena of reflection, refraction, interference and diffraction are common on both transverse and longitudinal waves, mechanical as well as electromagnetic. The distinguishing feature is that only transverse waves can be polarized. In an unpolarized light, the electric field vector has all the possible orientations in a plane perpendicular to the direction of propagation. When this light is passed through a specially cut crystal of calcite or quartz, called a polaroid, we obtain a plane polarized light. Only transverse waves can be polarized. Longitudinal waves cannot be poarlized.
Polarization by Reflection: Brewster’s Angle
In 1808, the French physicist Brewster discovered that when a beam of ordinary unpolarized light is incident at a particular angle ip on the surface of a transparent medium, the reflected light is polarized.
Figure shows an unpolarized light incident at an angle ip at the surface of glass. Brewster discovered that when i = ip, the reflected and refracted rays are exactly 90° apart. The angle ip when this happens is called the polarizing or the Brewster angle. If rp is the corresponding angle of refraction, then from the geometry of Fig.
Now from Snell’s law, the refractive index of glass is
This equation is called the Brewster law and the angle ip satisfying this equation is the Brewster angle.
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