Comprehensive Notes on Polarization (Ph 1109)
I. Polarization by Reflection & Brewster’s Law
Core Concept: Polarization by reflection occurs when ordinary light hits a plane surface (like glass). This was discovered by Malus in 1808.
| Term/Law | Definition/Value | Formula/Visual Aid |
|---|---|---|
| Polarizing Angle (i_p) | The angle of incidence where light is completely extinguished in the reflected path. For glass, this angle is 57.5∘. | ip=57.5∘ (for glass) |
| Brewster’s Law | The tangent of the angle of polarization (ip) is numerically equal to the refractive index (μ) of the medium. | tan(ip)=μ (Eq 2) |
| Reflected & Refracted Rays | When light is incident at ip, the reflected ray (BC) and the refracted ray (BD) are perpendicular to each other. | Reflected ⊥ Refracted (Implied ∠=90∘) |
Previous Year Questions: Polarization by Reflection
| Question (Year) | Subtopic | Hint/Steps Toward Solution |
| What is polarization of light? Discuss Brewster’s law and hence show that the reflected and refracted rays are 90∘ apart. (2018) | Brewster’s Law, Definition | State Brewster’s law. Use Snell’s law (Eq 1) and compare it with Brewster’s law (Eq 2) to show the 90∘ relationship. Note: A formal definition of polarization is not explicitly provided, but the phenomenon (light obtained by reflection) is described. |
| Prove that in the case of polarization, the reflected and the refracted rays are right angles to each other. (2023, 2022, 2018) | Brewster’s Law | This is achieved by comparing Snell’s law and Brewster’s law. |
| State and explain the polarization by double refraction and Brewster’s law or polarization by reflection. (2024) | Polarization Methods | State Brewster’s law. Mention Malus’ discovery. Explain double refraction (Section III). |
| Calculate the Brewster’s angle of light which travels from air into the glass medium (μ=1.55). (2021) | Calculation | Use ip=arctan(μ). Substitute μ=1.55. |
| Refractive index of crown glass 1.52. Find polarizing angle. If polarizing angle is about 59.50∘, find refractive index of glass. (2023) | Calculation | Use tan(ip)=μ. Solve for ip using μ=1.52. Then solve for μ using ip=59.50∘. |
II. Malus’ Law
Core Concept: This law describes how the intensity of polarized light changes when passing through an analyzer.
| Term/Law | Definition/Explanation | Formula/Visual Aid |
| Malus’ Law | The intensity (I) of polarized light transmitted through an analyzer varies as the square of the cosine of the angle (θ) between the plane of transmission of the analyzer and the plane of the polarizer. | I∝Ecos2θ (where E is incident intensity) |
| Amplitude Component | If incident amplitude is a (OP), only the component acosθ (along OA) is transmitted through the analyzer. | a→acosθ (transmitted component) |
Previous Year Questions: Malus’ Law
| Question (Year) | Subtopic | Hint/Steps Toward Solution |
| What is Malus law and Brewster’s law? (2021) | Definitions | State the definition of Malus’ Law regarding intensity and cos2θ. State Brewster’s Law relating tan(ip) and μ. |
III. Double Refraction (Birefringence)
Core Concept: The phenomenon where a single ray of light splits into two refracted rays when passing through certain crystals, discovered by Erasmus Bartholinus in 1669. Calcite (CaCO3) or Iceland Spar exhibits this.
| Feature | Ordinary Ray/Image (O) | Extraordinary Ray/Image (E) | Relationship |
| Image Behavior | Remains stationary when the crystal is rotated. | Rotates with the rotation of the crystal. | |
| Refractive Index (\mu) | μo (Higher) | μe (Lower) | In calcite, μo>μe. |
| Velocity (V) | Vo (Less) | Ve (Greater) | Because μo>μe, Vo<Ve. |
| Optic Axis | Double refraction is absent when light enters along the optic axis. |
Crystal Structure: Calcite reduces to a rhombohedron with angles 101∘55′ and 78∘5′.
• Principal Section: A plane containing the optic axis and perpendicular to the opposite faces. It cuts the surface in a parallelogram with angles 109∘ and 71∘.
• Principal Plane (O-Ray): A plane drawn through the optic axis and the ordinary ray.
• Principal Plane (E-Ray): A plane drawn through the optic axis and the extraordinary ray.
Previous Year Questions: Double Refraction
| Question (Year) | Subtopic | Hint/Steps Toward Solution |
| How ordinary rays and extraordinary rays are distinguished? (2021) | Ray Differentiation | Distinguish based on their image behavior (stationary vs. rotating) and their velocity/refractive index relationship (Vo<Ve because μo>μe). |
IV. Nicol Prism
Core Concept: An optical device invented by William Nicol in 1828, used for producing and analyzing plane polarized light.
| Feature | Detail | Index Values |
| Material/Shape | Calcite crystal, length three times its breadth. The natural angle of 71∘ is grounded down to 68∘. | |
| Construction | The crystal is cut along plane AKGL and the two halves are cemented with Canada balsam. | μordinary=1.658 |
| Cement Index | The refractive index of Canada balsam (μB=1.550) lies between μo and μe. | μbalsam=1.550 |
| Mechanism | The ordinary ray encounters the Canada balsam layer, which causes it to undergo total internal reflection (TIR) because μo>μB. The extraordinary ray is transmitted. | μextraordinary=1.486 |
| Function | Used as a polarizer (produces polarized light) and an analyzer (detects/tests polarized light). |
Previous Year Questions: Nicol Prism
| Question (Year) | Subtopic | Hint/Steps Toward Solution |
| Discuss the constructional details of a Nicol prism. How can you use it as a polarizer and an analyzer? (2017) | Construction/Use | Describe the grinding (71∘→68∘) and the use of Canada balsam cement. State its dual role in producing and detecting plane polarized light. |
| What is Nicol prism? How can it be used as a polarizer or as an analyzer? (2023) | Definition/Use | Define it as an optical device used for producing and analyzing plane polarized light. |
| What do you mean by a polarizer and an analyzer? Write down the applications of polarization. (2022) | Polarizer/Analyzer | Polarizer produces light; analyzer detects or tests light. Note: Applications are not listed in the source material. |
V. Optical Activity & Specific Rotation
Core Concept: The property of certain substances (like quartz) to rotate the plane of vibration of plane polarized light. This rotation depends on the plate thickness and the wavelength of light.
| Rotation Type | Direction | Observer’s View (Light towards observer) |
| Dextrorotatory | Rotates plane to the right. | Clockwise direction. |
| Laevorotatory | Rotates plane to the left. | Anti-clockwise direction. |
| Mechanism | Rotation occurs inside the body of the plate, not on its surface. |
Specific Rotation: Defined as the rotation produced by a 1 decimeter (10 cm) long column of the liquid containing 1 gram of the active substance in 1 cubic centimeter (cc) of the solution. This is used for determining the specific rotation of sugar solution.
Previous Year Questions: Optical Activity
| Question (Year) | Subtopic | Hint/Steps Toward Solution |
| What is specific rotation of an optically active substance? Discuss the determination of specific rotation of sugar solution by means of a polarimeter. (2019) | Specific Rotation | State the definition based on 1 decimeter length and 1 gm/cc concentration. Mention the use of a polarimeter for determination. |
| What do you mean by specific rotation? (2023) | Definition | State the definition based on length and concentration. |
| Calculate the specific rotation of a given sample of sugar solution… (2017, 2019) | Calculation | Use the specific rotation definition relating the observed angle (26.4∘), length (20 cm), and concentration (20% sugar solution). Note: The mathematical formula for this calculation is not explicitly provided in the source material. |
VI. Summary of Missing Concepts and Unrelated Questions
| Concept/Question | Status in Source Material |
| Definition of Polarization | Contextual explanation provided, but a formal definition is missing. |
| Applications of Polarization | Not listed in the source material. |
| Proof: Light is a Transverse Wave (2017) | Not discussed or proven in the source material. |
| Specific Rotation Calculation Formula | The definition is given, but the required mathematical formula (Length×ConcentrationRotation angle) is not explicitly shown. |
Compact Summary Points
• Brewster’s Law: Relates the polarizing angle (ip) to refractive index (μ) via tan(ip)=μ.
• Malus’ Law: Governs intensity (I) of transmitted polarized light: I∝cos2θ.
• Double Refraction: Splits light into Ordinary (μo) and Extraordinary (μe) rays; in calcite, μo>μe.
• Nicol Prism: Uses Canada balsam (μB=1.550) to cement calcite, causing the O-ray to undergo TIR and transmitting the E-ray.
• Specific Rotation: A measure of optical activity based on a 1 decimeter column containing 1 gm/cc of substance.