Brewster's angle

Brewster's Angle Experiment

1. BREWSTER’S ANGLE

2. AIM To study the polarization of light by simple reflection that is to study Brewster's law.

3. APPARATUS REQUIRED He laser D ial fitted polarizer Photo detector Micro ammeter Rotational mount Glass plate Constant power supply

4. THEORY BEHIND THE EXPERIMENT When light moves between two media of differing refractive index (n), some of the light is reflected from the surface of the denser material. This reflected ray’s intensity changes with change in the incident angle ( ) at the interface of two mediums. At one specific angle of incidence of light only perpendicular vibrations of electric field vectors are reflected whereas parallel vibrations are restricted or polarized. This loss in light intensity is due to polarization by reflection and the angle of incidence for which reflected ray is polarized is called the Brewster's angle θ B (also known as the Polarization angle). The fraction of the incident light that is reflected depends on both the angle of incidence and the polarization direction of the incident light. The functions that describe the reflection of light polarized parallel and perpendicular to the plane of incidence are called the Fresnel Equations. According to the Fresnel Law when light moves from a medium of a given refractive index ( ) into a second medium with refractive index ( ), both reflection and refraction of the light may occur.  

5. Definition of Brewster's Angle The angle of incidence at which light with a particular polarization is perfectly transmitted, without any reflection. When unpolarized light is incident at this angle, the reflected signal would be perfectly polarized:

6. Derivation of Brewster's Angle At Brewster's Angle, the reflected and transmitted waves must be orthogonal To find Brewster's Angle, solve for  θ in the following equations: θ = 90˚ -  θ1 θ1 + θ2 = 180˚ - 90˚ = 90˚ θ1 = θ1 *sin( θ1) = *sin( θ2) θ =  

7. Fresnel Equations & Brewster's Law The portion of a wave reflected when it encounters a boundary between two media is described by the Fresnel equations The Fresnel equations predict that light with p polarization will not be reflected if the angle of incidence is   where and are the indices of refraction of the media This relationship is known as Brewster's Law  

8. Fresnel Equations & Brewster's Law

9. EXPERIMENTAL SETUP

10. PROCEDURE Set up the system shown In figure. Be sure the glass reflecting material is vertical and centered over the axis of rotation of the rotational stage. Glass reflecting material was setup such that at 90° on the protractor, the incident ray (from a red He Laser source) hit the surface perpendicularly so the reflected beam goes back into the laser aperture. Be sure that the rotational stage reads 0o at this point. Darken the room as much as possible. Adjust the laser so the output is horizontally polarized. The protractor is then rotated to angle values less than 90° in an interval of 5o . The reflected ray is directed to a fiber optic light intensity sensor which measures the intensity of the reflected light in terms of current. Record the current in micro ammeter . This alignment of the incoming laser and the protractor ensures that the angle on the protractor equals the angle of the incident ray, thus gives the value of the incidence angle. The angle range is limited between 20° and 80° because of the expanse of the fiber optic light intensity sensor holder. Between the angles of 50o and 60o , measure the intensity of reflected beam in 2o increment. You will notice that at a certain angle, Brewster’s angle, there will be little or no reflected light. Record this angle.

11. observations

12. Data Analysis Applying Brewster's Law, we can now determine the index of refraction of the styrene pellets Since it is known that :            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 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.  

13. Plot of power (current I) vs angle ‘𝜽’

14. Precaution The laser beam should not penetrate into eyes as this may damage the eyes permanently. The photo detector should be as away from the slit as possible. The laser should be operated at a constant voltage 220V obtained from a stabilizer. This avoids the flickering of the laser beam. Laser should be started at least 15 minutes before starting the experiment. Scale of Vernier should be rotated slowly. Room should be perfectly dark.

15. Application: Polaroid Sunglasses Glare consists almost entirely of horizontally polarized light. Vertically polarized light is useful for human vision. Polarized sunglasses can selectively block certain polarizations of light.

16. Application: Polarized Camera Lenses Unpolarized                                  Polarized

17. Application: Brewster Windows Whenever a wave passes through a transparent window, some degree of optical loss will occur. Even with an anti-reflective coating, a normal glass pane will have a reflectivity of around 0.2% on each side. Brewster windows are tilted to create an angle of incidence close to Brewster's angle. Result in at least 10 times lower losses.

18. Application: Brewster Angle Microscopy Used to detect changes in refractive index on water surface. Water surface does not reflect light, appears black. When surfactants alter the refractive index, Brewster's Angle changes locally and a reflected wave is observable

19. Demonstrations Mathematica plot of absorbed/reflected light https://demonstrations.wolfram.com/FresnelEquations / Visual of polarized light hitting a medium at Brewster's Angle https:// vlab.amrita.edu/index.php?sub=1&brch=189&sim=333&cnt=4

20. refrences http://en.wikipedia.org/wiki/Brewsters_angle https://vlab.amrita.edu/? sub=1&brch=189&sim=333&cnt=2 https:// www.iitr.ac.in/departments/PH/uploads/Teaching%20Laboratory/12%20Brewsters%20angle.pdf