Comprehensive Note on Polarization
I. Polarization by Reflection and Malus’ Law
A. Polarization by Reflection
Polarization of light by reflection from a glass surface was discovered by Malus in 1808. He observed that polarized light is obtained when ordinary light is reflected by a plane sheet of glass.
If light is incident on a glass surface and the reflected light (along path BC) is observed through a rotating tourmaline crystal, it will be completely extinguished at only one specific angle of incidence. This angle, known as the polarizing angle, is 57.5∘ for a glass surface. Polarized light can also be produced by reflection from a water surface.
B. Brewster’s Law
Brewster performed experiments starting in 1811 to study polarization by reflection.
1. Refractive Index Relation: Brewster proved that the tangent of the angle of polarization (θp) is numerically equal to the refractive index (μ) of the medium (tan(θp)=μ).
2. Ray Perpendicularity (Intuitive Visual): When unpolarized light is incident at the polarizing angle, the reflected ray (→ BC) and the refracted ray (→ BD) are perpendicular to each other (90∘ apart).
C. Malus’ Law
Malus’ law describes the intensity variation when polarized light passes through an analyzer.
• Statement: The intensity of the polarized light transmitted through the analyzer (I) 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.
• Relation: If E is the intensity of incident polarized light, the transmitted intensity is I∝Ecos2θ. Only the component of amplitude acosθ is transmitted through the analyzer.
| Previous Year Questions (Reflection/Laws) | Year(s) | Hint/Steps |
| What is Malus law and Brewster’s law? | 2021 | State Malus’ law and Brewster’s law (tan(θp)=μ). |
| Discuss Brewster’s law and hence show that the reflected and refracted rays are 90° apart. | 2018 | State Brewster’s law. Use Snell’s law and compare it with Brewster’s law to show the 90∘ relationship. |
| Prove that in the case of polarization, the reflected and the refracted rays are right angles to each other. | 2023, 2022, 2018 | Use the expressions for Snell’s law and Brewster’s law. |
| Calculate the Brewster’s angle of light which travels from air into the glass medium (μ=1.55). | 2021 | Apply Brewster’s law: θp=tan−1(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 | Use θp=tan−1(1.52) for the first part, and μ=tan(59.50∘) for the second part. |
II. Double Refraction
A. Phenomenon and Crystal
Double refraction was discovered by Erasmus Bartholinus in 1669. It occurs when a ray of light is refracted by a crystal of calcite, yielding two refracted rays.
• Calcite: Also known as Iceland spar, it is crystallized calcium carbonate (CaCO3). It can be reduced into a rhombohedron bounded by six parallelograms with angles of 102∘ and 78∘.
• Observation: If a calcite crystal is placed over an ink dot, two images are observed. When the crystal is rotated, one image (the ordinary image) remains stationary, and the other (the extraordinary image) rotates.
• Rays: Double refraction is absent when light enters the crystal along the optic axis.
◦ Ordinary Ray (O-ray): Has a refractive index μo.
◦ Extraordinary Ray (E-ray): Has a refractive index μe.
• Velocity: For calcite, μo>μe. Therefore, the velocity of the O-ray inside the crystal is less compared to the velocity of the E-ray.
B. Principal Sections and Planes
• Principal Section: A plane that contains the optic axis and is perpendicular to the opposite faces of the crystal. A crystal has three principal sections for every point.
• Principal Plane (Ordinary Ray): A plane in the crystal drawn through the optic axis and the ordinary ray.
• Principal Plane (Extraordinary Ray): A plane in the crystal drawn through the optic axis and the extraordinary ray.
• The two principal planes generally do not coincide.
| Previous Year Questions (Double Refraction) | Year(s) | Hint/Steps |
| State and explain the polarization by double refraction… | 2024 | Explain the process: one incident ray splits into two (O-ray and E-ray) upon entering calcite. |
| How ordinary rays and extraordinary rays are distinguished? | 2021 | Use the stationary vs. rotating image test. Note that μo>μe, meaning O-ray velocity is slower than E-ray velocity. |
III. Nicol Prism
The Nicol prism is an optical device invented by William Nicol in 1828. It is used for producing and analyzing plane polarized light.
A. Construction
1. A calcite crystal is used (length three times its breadth).
2. The face angles are ground from 71∘ to 68∘.
3. The crystal is cut along a specific plane (AKGL).
4. The two cut surfaces are polished and cemented together using Canada balsam.
5. Refractive Indices: Calcite μo=1.658, μe=1.486. Canada balsam μB=1.550. The Canada balsam’s refractive index lies between those of the ordinary and extraordinary rays. This allows the separation of the two rays via total internal reflection of the O-ray.
B. Use
The Nicol prism can be used for the production and detection of plane polarized light. It acts both as a polarizer and an analyzer.
| Previous Year Questions (Nicol Prism) | Year(s) | Hint/Steps |
|---|---|---|
| Explain how a Nicol prism produces plane polarized light. | 2016 | Describe the construction details (angles, Canada balsam) and explain how the O-ray is eliminated due to total internal reflection via the intermediate refractive index (μB vs μo, μe). |
| Discuss the constructional details of a Nicol prism. How can you use it as a polarizer and an analyzer? | 2017 | Detail the grinding (e.g., 71∘→68∘) and the cementing with Canada balsam. Mention its role in production and detection. |
| What is Nicol prism? How can it be used as a polarizer or as an analyzer? | 2023 | Define it as an optical device for producing and analyzing plane polarized light. |
IV. Optical Activity and Specific Rotation
A. Optical Activity
Optical activity is the property of certain crystals or substances (like a quartz plate) to rotate the plane of vibration of plane polarized light.
• The rotation occurs inside the body of the plate, not on its surface.
• The amount of rotation depends on the thickness of the plate and the wavelength of light.
• Dextrorotatory (Right-Handed): Substances that rotate the plane of vibration clockwise when the observer looks towards the light source.
• Laevorotatory (Left-Handed): Substances that rotate the plane of vibration anti-clockwise.
B. Specific Rotation
Specific rotation is 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.
| Previous Year Questions (Optical Activity/Specific Rotation) | Year(s) | Hint/Steps |
| What is specific rotation of an optically active substance? Discuss the determination of specific rotation of sugar solution by means of a polarimeter. | 2019 | Define specific rotation. Note: The detailed procedure for determination using a polarimeter is not explicitly provided in the source slides. |
| What do you mean by specific rotation? | 2023 | Provide the definition relating rotation to length (10 cm) and concentration (1 gm/cc). |
| Calculate the specific rotation of a given sample of sugar solution if the plane of polarization is turned through 26.4°. The length of the tube containing 20% sugar solution is 20 cm. | 2017, 2019 | Apply the definition using the length (20 cm → 2 dm) and concentration (20% → relevant concentration in gm/cc). Note: The explicit formula for calculation is not provided in the source slides. |
V. Missing Definitions and Concepts
The sources do not contain explicit definitions for the following concepts required by the previous-year questions:
1. Polarization of light (General definition).
2. Polarizer and Analyzer (Formal definitions).
3. Applications of polarization.
4. Proof that light wave is a transverse wave.
5. The explicit formula or the step-by-step discussion of determining specific rotation of sugar solution by means of a polarimeter.