Find out expression for fringe width in Young's double slit experiment.

Young’s double slit experiment demonstrated the phenomenon of interference of light Consider two coherent sources of light S 1 and S 2 are placed at a distance d apart and a screen is placed at a distance D from the two sources. Let P be a point on the screen at a distance y from the centre of the screen. If x is the path difference between the light waves then, x = S 2 P - S 1 P In right-angled ∆ S 2 B P , we have S 2 P 2 = S 2 B 2 + B P 2 = D 2 + y + d 2 2 Also in right-angled ∆ S 1 A P , we have S 1 P 2 = S 1 A 2 + A P 2 = D 2 + y - d 2 2 Thus, S 2 P 2 - S 1 P 2 = D 2 + y + d 2 2 - D 2 + y - d 2 2 or ( S 2 P + S 1 P ) ( S 2 P - S 1 P ) = y + d 2 2 - y - d 2 2 Since, S 2 P - S 1 P = x (the path difference) Thus, ( S 2 P + S 1 P ) · x = 4 y · d 2 = 2 y d or x = 2 y d S 2 P + S 1 P In practice, S 2 P ≈ S 1 P ≈ D Hence, x = 2 y d 2 D or x = y d D . This is the expression for path difference. The point P will be a centre of bright fringe, if y d D = n λ or y = n λ D d , where, n = 0 , 1 , 2 , 3 , . . . . . . . Similarly, the point P will be a centre of dark fringe, if y d D = ( 2 n + 1 ) λ 2 or y = ( 2 n + 1 ) λ D 2 d , where, n = 0 , 1 , 2 , 3 , . . . . . . . The spacing between any two consecutive bright fringes or dark fringes is called fringe width. It is represented by β . Thus, β = y n - y n - 1 = n λ D d - ( n - 1 ) λ D d = λ D d (for bright fringe) and β ' = y n ' - y n - 1 ' = ( 2 n + 1 ) λ D 2 d - 2 n - 1 + 1 · λ D 2 d = λ D d (for dark fringe) Thus, it is clear that, β = β '

What is polarisation by reflection. Deduce Brewster's law.

Polarisation By Reflection: If light incidents on a refractive surface so that the refracted light and the reflected light are at 90 ° angle, then the reflected light will be linearly polarised, and the plane of polarisations will be parallel to the plane of the interface. As per the Brewster’s Law, the maximum polarisation takes place when the angle is 90 degrees in between the reflected ray and refracted ray. The polarizations angle is called Brewster’s angle. In this case μ = tan I p where I p = Brewster 's angle Refer to the figure , when light is incident at polarising angle p on a refracting medium of refractive index μ , Let r be the angle of refraction, then according to the Snell's law. μ = sin I p sin r and from the brewster's Law sin I p sin r = tan p or sin p sin r = sin p cos p or sin r = cos p or sin r = sin ( 90 - p ) or r = 90 - p or r + p = 90 . Hence, when a ray of light incident at the polarising angle, the reflected ray is perpendicular to the refracted ray. This is Brewster's law.

What is the shape of the wavefront for the light diverging from a point source?

Wavefront is defined as the locus of all points in a wave motion having same phase. When the light diverges from a point source the shape of the wavefront is spherical as the light diverges from a point source in all directions.every point on the waveform is equidistant from the point source. Every point on this spherical waveform will have the same phase.

Using Huygens' construction, explain reflection of a plane wave by a plane surface

Huygens' principle states that every point on a wavefront is in itself the source of spherical wavelets. The sum of these spherical wavelets forms the wavefront. Explanation of reflection by Huygens principle: In the above figure AB is the incident wavefront on a plane mirror at an angle ∠ BAA ' = i . According to Haugen's principle, every point on AB is a source of secondary waves. Let the secondary wavelet from B strikes the mirror at A ' in t sec. so BA ' = c × t .............................(1) c = velocity of light, The secondary wavelets rrom A will travel the same distance at the same time. Draw a radius c × t with A as centre, draw an arc B ' so that A B ' = C × t .........................(2) From A ' , draw a tangent plane A ' B ' touching the spherical arc tangentially at B ' , therefore A ' B ' is the secondary wavelets after time t . This would advance in the direction 1 ' , 2 ' , 3 ' which are corresponding reflected rays. Thus A ' B ' is the reflected wavefront.So we have, Incident wavefront= AB , reflected wavefront= A ' B ' . In △ AA ' B and AA ' B ' , A A ' is common , BA ' = AB ' = c × t and ∠ B = ∠ B ' = 90 ° Hence the triangles are congruent so ∠ BAA ' = ∠ B ' A ' A i . e ∠ i = ∠ r ............(A) This is the first law of reflection. Further, the incident and the reflected wavefront both are perpendicular to the paper. Therefore, the incident ray, normal to the mirror and the reflected ray all is in the same plane.this is the second law of reflection

What is interference of light waves. State two essential conditions to observe it.

Interference is the phenomenon in which two waves superpose to form the resultant wave of the lower, higher or same amplitude.In this phenomenon, the light energy is redistributed.in a medium on account of superposition of light waves from two coherent sources. The essential conditions for interference to occur are: (1) The sources of the waves must be coherent, which means they emit identical waves with a constant phase difference in the same direction. (2) The waves should be monochromatic - they should be of a single wavelength.

What is the geometrical shape of the wavefront for light emerging out of a convex lens when a point-source is placed at the focus of the lens?

The shape of the wavefront in case of a light emerging out of a convex lens when a point source is placed at its focus is a parallel wave front as shown in the figure. The light from the source at the focus of a lens will emerge parallel and will form a plane wave front following the Huygens' principle.