--- title: "Double refraction, linear and circular light" subject: "Engineering Physics" chapter: 4 key: "semester_1/engineering_physics:double-refraction-produce-polarized-light" source: https://www.bctengineer.com/q/semester_1/engineering_physics/double-refraction-produce-polarized-light site: BCT Engineering --- # Double refraction, linear and circular light Engineering Physics · Chapter 4: Physical Optics - Asked in: 2074 Asoj, 5 marks - Video: [Optic Axis and Birefringence](https://www.youtube.com/watch?v=5GSgji6zf00) — Reumi's world - Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14 - Page: https://www.bctengineer.com/q/semester_1/engineering_physics/double-refraction-produce-polarized-light - Whole chapter: https://www.bctengineer.com/md/semester_1/engineering_physics/chapter-4 ## Question What is double refraction? Explain how would you use the phenomenon to produce linear polarized light and circularly polarized light. ## Short answer Double refraction splits unpolarized light into ordinary and extraordinary rays with perpendicular polarizations. Linearly polarized light is obtained by removing the o-ray using a Nicol prism. Circularly polarized light is produced by passing plane-polarized light through a quarter-wave plate with its vibration direction at 45° to the optic axis, so equal-amplitude components acquire a 90° phase difference. ## Answer **Double refraction** is the splitting of a ray of unpolarized light into two plane-polarized rays on entering an anisotropic crystal such as calcite or quartz. The **ordinary (o) ray** obeys Snell's law and has the same speed in all directions. The **extraordinary (e) ray** does not obey Snell's law and its speed depends on direction. Their vibrations are perpendicular. Along the optic axis there is no double refraction. #### Linearly polarized light 1. Pass natural light through a calcite crystal (or Nicol prism). The two emergent rays are plane polarized perpendicular to each other. 2. In a Nicol prism the o-ray is removed by total internal reflection at the Canada balsam layer, so only the e-ray, which is plane polarized, emerges. 3. Alternative: use a tourmaline plate, which absorbs the o-ray. #### Circularly polarized light ```text unpolarized -> [Nicol]-> plane pol. -> [QWP, axis at 45°] -> circular (A) a = b = A/√2, δ = 90° ``` 1. Plane polarized light of amplitude A falls on a quarter-wave plate (a crystal plate cut parallel to the optic axis), with its vibration at **θ = 45°** to the optic axis. 2. It splits into e and o components: a = A cos 45° and b = A sin 45°, so a = b = A/√2. 3. The plate thickness is chosen so that the path difference is λ/4, i.e. phase difference δ = π/2: t = λ / [4(μ_o − μ_e)]. 4. With x = a cos ωt and y = a sin ωt (quadrature), the resultant is x² + y² = a², a circle. Hence the emergent light is **circularly polarized** (right or left handed depending on which ray is faster). If θ ≠ 45° with the same plate, the light is elliptically polarized. ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. Double refraction is: A. Splitting of unpolarized light into two plane-polarized rays in an anisotropic crystal B. Reflection twice inside a prism C. Bending of light around a slit D. Refraction in two liquids Answer: A. An anisotropic crystal like calcite splits a ray into o and e rays with perpendicular vibrations. (Key point: Double refraction) 2. Which statement about the rays is correct? A. The e-ray obeys Snell's law; the o-ray does not B. The o-ray obeys Snell's law and has the same speed in all directions C. Both obey Snell's law D. Both have vibrations parallel to each other Answer: B. The o-ray obeys Snell's law with direction-independent speed; the e-ray does not. (Key point: Ordinary vs extraordinary) 3. How does a Nicol prism give plane polarized light? A. It absorbs the e-ray B. The o-ray is removed by total internal reflection at the Canada balsam layer C. It rotates the o-ray by 90° D. It combines both rays Answer: B. The o-ray is totally reflected at the balsam layer, leaving only the plane polarized e-ray. (Key point: Nicol prism) 4. How is circularly polarized light produced from plane polarized light? A. Quarter-wave plate with vibration at 45° to the optic axis B. Half-wave plate at 0° C. Quarter-wave plate with vibration along the axis D. Quarter-wave plate at 30° Answer: A. At 45° the e and o components have equal amplitudes a = b = A/√2, and the λ/4 plate gives δ = 90°, so x^2 + y^2 = a^2. (Key point: Circular polarization) ## Related in Engineering Physics - [Production of plane, circular, elliptical light](https://www.bctengineer.com/question.md?key=semester_1%2Fengineering_physics%3Apolarized-light-production-relations) — Engineering Physics, chapter 4, asked 3× - [Distinguishing plane, circular, elliptical light](https://www.bctengineer.com/question.md?key=semester_1%2Fengineering_physics%3Adistinguish-polarized-nicol-wave-plate) — Engineering Physics, chapter 4 - [Index difference for circular polarization](https://www.bctengineer.com/question.md?key=semester_1%2Fengineering_physics%3Aqwp-refractive-index-difference) — Engineering Physics, chapter 4 ## Related in other subjects - [Circular well 4 m, light and heavy well](https://www.bctengineer.com/question.md?key=semester_5%2Ffoundation_engineering%3Acircular-well-4m-light-heavy) — Foundation Engineering, chapter 9 - [Circular queue vs linear queue](https://www.bctengineer.com/question.md?key=semester_4%2Fdata_structure_and_algorithm%3Acircular-vs-linear-queue) — Data Structure and Algorithm, chapter 2 - [Linear and circular queue operations](https://www.bctengineer.com/question.md?key=semester_4%2Fdata_structure_and_algorithm%3Alinear-circular-queue-algorithms) — Data Structure and Algorithm, chapter 2 - [Linear convolution via circular convolution](https://www.bctengineer.com/question.md?key=semester_7%2Fdigital_signal_analysis_and_processing%3Alinear-conv-via-circular) — Digital Signal Analysis and Processing, chapter 7