Brewster law

verification of brewsters law

1. BREWSTER’S LAW

2. OUTLINE OF THE EXPERIMENT Aim of experiment Apparatus required Theory behind experiment Outline of experiment Procedure Observations (tabular column) Graph Conclusion( result)

3. AIM : To study the polarization of light by simple reflection that is to study brewester’s law .

4. APPARATUS REQUIRED : A rectangular metallic box with diode laser fitted on one side and photon detector is mounted on an arm which may be rotated co axially with respect to rotation of a turn table with index line to read angle of rotation with respect to graduated disc fitted at the middle of the top plate of rectangular box. A pile of glass plates is fixed on top of turn table. Glass plates Digital meter reading Diode laser Photon detector

5. THEORY BEHIND EXPERIMENT E.L Malus French Engineer discovered in 1808 polarization of light by reflection. He Noticed that when natural light is incident on a smooth surface at a certain angle the Reflected beam is plane polarized. The extent to which polarization occurs is dependent Upon the angle at which the light is incident on surface is made of metallic surfaces Reflected light with variety of vibrational directions, such reflected light is unpolarized . However, light that is specularly reflected from dielectric surfaces such as asphalt road Ways, water etc,as linearly polarized.

6. Let us consider an light wave that is electromagnetic wave made up of mutually perpendicular, fluctuating electric and magnetic fields .the polarization of electromagnetic wave is taken as the direction of direction electricfield vector. So the light wave can be described by the electric field vector. When a light wave the unpolarized light is incident on a boundary between two dielectric materials (glass & air) .there always be a reflected ray and refracted ray. The electric vector of the ray can be resolved into two components. One is perpendicular to plane and the other is parallel to plane of incidence. The perpendicular components are represented by dots “.” is called s-component .the parallel components are represented by arrows “ ”is called p-polarization.

7. In case of completely un polarized light the components are of equal magnitude. From electromagnetic waves we know that it contains mutually perpendicular electric & magnetic fields . By considering the components of the fields let us derive an expression . we will assume that electric vector to lie in the plane of incidence & magnetic vectors are along y-axis . Clearly z-components of electric fields represent a tangential components which should be continous across the surface. E1z + E3z = E2z -E1cos θ 1 + E3cos Ѳ 1 = -E2cos Ѳ 2---------------->(1) Once again, since this condition has to be Satisfied at all points in space X=0 (E1-E3) cos Ѳ 1 = E2cos Ѳ 2------------------- >(2) Further , the normal component of D must also Be continous and since D= ε E we must have , ε1E1x + ε 1E3x = ε 2E2x------------------>(3)

8. ε 1(E1+E3) sin Ѳ 1 = ε 2E2sin Ѳ 2--------------- >(4) Substituting E2 from equation (3) we get ε1(E1+E3)sin Ѳ 1 = ε 2sin Ѳ 2 (E1-E3)/ cos Ѳ 2 cos Ѳ 2 ( E2sin Ѳ 2cos Ѳ 1 + E1sin Ѳ 1cos Ѳ 2)E3 = ( ε 2sin Ѳ 2cos Ѳ 1- ε 1sin Ѳ 1cos Ѳ 2)E1 Thus r ll = E3/E1 = ε 2sin Ѳ 2cos Ѳ 1- ε 1sin Ѳ 1cos Ѳ 2/ ε 2sin Ѳ 2cos Ѳ 1+ ε 1sin Ѳ 1cos Ѳ 2-------------->(5) Where r denotes the amplitude reflection co efficient and subscript ‘ll’ represents parallel polarization. And the expression for amplitude reflection co efficient simplifies to r ll = n 2 2 sin Ѳ 2cos Ѳ 1-n 2 1 sin Ѳ 1cos Ѳ 2/n 2 2 sin Ѳ 1cos Ѳ 2

9. From snell’s law we know that sin Ѳ 1/sin Ѳ 2 = n2/n1 We get r ll = n2cos Ѳ 1-n1cos Ѳ 2/n2cos Ѳ 1+n1cos Ѳ 2 again by using snell’s law r ll = sin Ѳ 1cos Ѳ 1-sin Ѳ 2cos Ѳ 2/sin Ѳ 1cos Ѳ 1+sin Ѳ 2cos Ѳ 2 r ll = tan( Ѳ 1- Ѳ 2)/ tan ( Ѳ 1 + Ѳ 2) ---------------- >(7) N ow by considering a special case Ѳ 1+ Ѳ 2 = 90°. The denominator of equation (7) becomes infinetly large so r ll = 0 That is there is no reflected beam. Thus if an un polarized beam is incident at an angle such that Ѳ 1+ Ѳ 2 =90°. Then the parallel component of the E-vector will not be reflected and reflected light will be polarized with its E-vector perpendicular to plane of incidence . We can say that reflected light is plane polarized .

10. From snell’s law, sin Ѳ 1/sin Ѳ 2 =n2/n1 sin Ѳ 1/ cos Ѳ 1 =n2/n1 ( Ѳ 1+ Ѳ 2=90 °) tan Ѳ 1 = n2/n1 Ѳ 1 = tan -1 (n2/n1) This is known as brewesters angle . BREWSTERS LAW – tangent of the angle at which polarization is obtained by reflection is numerically equal to refractive index of the medium. Thus ,when the angle of incidence is equal to tan -1 (n2/n1) then the reflected beam is plane polarized.

11. Pile of Glass plates Digital meter reading Diode laser Photon detector EXPERIMENTAL SETUP

12. PROCEDURE : Diode laser light is allowed to incident on the glass plate and the reflected light is received by the photon detector. Note the reading in the digital meter which is provided on the front panel. Now rotate the turn table (manually) with the increment of 5° and so on and take the readings of the reflected light received by the detector .it is evident that the angle of incidence ( Ѳ ) the reflected light received at 2 Ѳ . At an angle of 57° the plane of vibration of beam is perpendicular to the plane of incidence . Hence intensity received by photo detector is zero near zero. Graph is plotted between angle of incidence and amount of light received by detector to prove brewsters law.

13. Angle of incidence (i)degree Digital meter reading 5 10 15 20 25 30 35 40 45 50 55 60 65 70 1.76 1.14 0.83 0.68 0.61 0.55 0.49 0.34 0.23 0.20 0.08 0.19 0.44 0.51 observations

14. RESULT & CONCLUSION From the graph, brewster’s angle is Ѳ = 56°. We can conclude that if an un polarized light is incident at angle is equal to 56° then Reflected light will be plane polarized where reflected light does not contain E-vector parallel components , it contains only perpendicular components . We can tell that s-polarization involved in this experiment. Through digital meter set up we can easily find an brewster’s angle compared to spectrometer & very less time consuming.