Polarization and Double Refraction Concepts

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Questions and Answers

What happens to the ordinary and extraordinary waves at normal incidence in a crystal?

  • They interfere destructively, canceling each other out.
  • They travel in parallel directions with different velocities. (correct)
  • They separate into two distinct beams.
  • They merge into a single beam with no path difference.

Which equation represents the extraordinary ray's amplitude in terms of the incident amplitude and phase difference?

  • x = A sin(𝜃) sin(ωt)
  • x = A cos(𝜃) sin(ωt)
  • x = A cos(𝜃) sin(ωt + δ) (correct)
  • x = A sin(𝜃) sin(ωt + δ)

How is the amplitude of the ordinary ray expressed in the content?

  • A cos(θ) cos(ωt)
  • A cos(𝜃) sin(ωt + δ)
  • A sin(𝜃) sin(ωt) (correct)
  • A sin(θ) cos(ωt)

What is the relationship between x and y based on the equations provided?

<p>x/y = cos(δ) + √(1 - y2/b2) (D)</p> Signup and view all the answers

What effect does the angle θ have on the amplitudes of the ordinary and extraordinary rays?

<p>It determines both amplitudes, introducing a phase difference. (A)</p> Signup and view all the answers

In the derived equations for x and y, what represents the phase difference?

<p>δ (B)</p> Signup and view all the answers

What characteristic of polarized light is utilized in quarter wave and half wave plates?

<p>The different velocities and phase shifts of the ordinary and extraordinary rays. (D)</p> Signup and view all the answers

What is denoted as A in the context of the incident plane polarized light?

<p>The amplitude of the incident plane polarized light. (B)</p> Signup and view all the answers

What is 'unpolarised light' characterized by?

<p>Vibrations in all directions (D)</p> Signup and view all the answers

Which method of polarization involves Malus's discovery?

<p>Polarisation by reflection (B)</p> Signup and view all the answers

What happens to unpolarised light when it passes through crystal A?

<p>Only vibrations parallel to the crystal's axis are transmitted (C)</p> Signup and view all the answers

When unpolarised light passes through a series of thin glass plates, what percentage of vibrations typically reflects?

<p>15% (C)</p> Signup and view all the answers

What is indicated by the term 'ordinary ray' in double refraction?

<p>The ray that vibrates in a plane parallel to the crystal axis (C)</p> Signup and view all the answers

In the context of polarization, what is the 'plane of vibration'?

<p>The direction of all polarized vibrations (B)</p> Signup and view all the answers

Which of the following methods does not lead to polarization?

<p>Scattering (A)</p> Signup and view all the answers

What is the result of polarization by double refraction?

<p>Two refracted rays are produced that are orthogonal (A)</p> Signup and view all the answers

What does the tangent plane CO represent in the context of the O-ray?

<p>Position of the O-wave front (A)</p> Signup and view all the answers

Which equation represents the relationship between the velocities of the ordinary ray and extraordinary ray?

<p>$V_e = \frac{V_a}{\mu_e}$ (A)</p> Signup and view all the answers

What occurs when O and E waves coincide at all instants under normal incidence?

<p>There is no double refraction (A)</p> Signup and view all the answers

In the case where the optic axis is perpendicular to the refracting surface, what happens during oblique incidence?

<p>The two wave fronts touch at a point (B)</p> Signup and view all the answers

What direction does the line AP represent in the oblique incidence scenario?

<p>Direction of the optic axis (D)</p> Signup and view all the answers

How do the O and E rays behave in the case where the optic axis is parallel to the refracting face under oblique incidence?

<p>They travel with different velocities along different directions (D)</p> Signup and view all the answers

Which plane represents the wave front of the E waves intersecting at point E?

<p>Plane CE (B)</p> Signup and view all the answers

What is indicated by the tangent planes OOl and EEl in normal incidence?

<p>They represent the wave fronts of O and E rays respectively (D)</p> Signup and view all the answers

What does a beam passing through a quarter wave plate and subsequently an N-prism indicate if it extinguishes completely twice during rotation?

<p>The beam is circularly polarized. (D)</p> Signup and view all the answers

What is the characteristic behavior of elliptically polarized light when passed through a rotating N-prism?

<p>Its intensity varies from maximum to minimum. (B)</p> Signup and view all the answers

What further phase difference do the O-ray and E-ray undergo when elliptically polarized light passes through a quarter wave plate?

<p>$ rac{ ext{π}}{2}$ (B)</p> Signup and view all the answers

What is the purpose of the Babinet's compensator?

<p>To introduce a desired path difference for varying wavelengths. (B)</p> Signup and view all the answers

What condition should be avoided when light is incident on a QWP to ensure it emerges elliptically polarized?

<p>At 45 degrees to the optic axis. (D)</p> Signup and view all the answers

After passing elliptically polarized light through a quarter wave plate, if the beam remains elliptically polarized, what does that imply?

<p>The incident beam was partially polarized. (A)</p> Signup and view all the answers

How can you distinguish between circularly polarized light and unpolarized light after passing through a quarter wave plate?

<p>Only circularly polarized light will extinguish completely upon rotation. (D)</p> Signup and view all the answers

In the context of light polarization, what indicates that a beam is partially polarized when observed through an N-prism?

<p>The beam shows some variation in intensity. (C)</p> Signup and view all the answers

What is the least thickness of the quartz plate required for plane polarized light to emerge plane polarized?

<p>2.778 × 10−5 m (B)</p> Signup and view all the answers

How is the thickness of a calcite plate for circularly polarized light calculated?

<p>Using the difference of refractive indices and wavelength. (B)</p> Signup and view all the answers

What is the required thickness of a calcite plate to convert plane polarized light into circularly polarized light?

<p>8.565 × 10−7 m (A)</p> Signup and view all the answers

What is the optical path difference produced by a crystal plate if the thickness is 1.5 × 10−5 m?

<p>1.5 × 10−7 m (C)</p> Signup and view all the answers

For circularly polarized light, what is the formula for calculating the thickness of a plate?

<p>t = λ / 4(μe − μ0) (C)</p> Signup and view all the answers

What is the rotation of the plane of polarization in a substance if the wavelength is 5890 × 10−10 m?

<p>7.62 × 10−8 (D)</p> Signup and view all the answers

Which of the following factors affects the optical path difference in a crystal plate?

<p>All of the above (D)</p> Signup and view all the answers

What determines whether a light beam will become circularly polarized when passing through a material?

<p>Both A and B (C)</p> Signup and view all the answers

What is the relationship between phase difference and path difference in a wave?

<p>Phase difference is proportional to path difference. (D)</p> Signup and view all the answers

How is the wavelength calculated from phase difference and path difference?

<p>Wavelength can be determined using the formula λ = t(μL - μR) / φ. (D)</p> Signup and view all the answers

When given a concentration of a solution and the length of the polarimeter tube, how is the rotation of the plane of polarization calculated?

<p>Rotation is calculated as the product of specific rotation, length, and concentration. (B)</p> Signup and view all the answers

If a polarimeter tube produces an optical rotation of 240 with a specific rotation of S, what quantity is needed to determine S?

<p>All of the above. (D)</p> Signup and view all the answers

What is the phase difference when the path difference is 5890 x 10-10 and the thickness of the material is 2m in given conditions?

<p>0.8125 radians. (A)</p> Signup and view all the answers

In the case of a sugar solution with a concentration of 100 kgm-3, what does the specific rotation of the sugar represent?

<p>The ratio of angle rotated to the concentration and length. (D)</p> Signup and view all the answers

When calculating the rotation of the plane of polarization in a polarimeter, what incorrectly describes the process?

<p>The specific rotation has no impact on the measured rotation. (A)</p> Signup and view all the answers

If a solution has a specific rotation of 0.750 kg-1m2 and its concentration is given, what information would not change the calculation of the plane rotation?

<p>Material the tube is made from. (D)</p> Signup and view all the answers

Flashcards

Unpolarized light

Light with vibrations in all directions.

Polarized light

Light with vibrations in one direction.

Plane of vibration

The plane containing the direction of light wave vibrations.

Plane of polarization

The plane perpendicular to the plane of vibration.

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Polarization by reflection

Producing polarized light by reflecting light off a surface.

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Polarization by refraction

Producing polarized light by passing light through multiple parallel plates.

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Polarization by double refraction

Producing polarized light by passing light through a crystal like calcite.

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Ordinary ray

One of the two refracted rays produced by double refraction.

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Extraordinary ray

The other refracted ray in double refraction.

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Selective Absorption

Lights passing through a crystal that absorbs all vibrations except those parallel to the crystal's axis.

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Transverse nature of light

Light exhibits variations in intensity when passing through polarized crystal, indicative of its transverse wave nature.

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Double Refraction (Birefringence)

The splitting of a single light ray into two rays with different velocities as it passes through certain crystals.

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Ordinary Ray (O-ray)

Light ray that travels with a constant velocity, following Snell's law (refracting according to refractive index).

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Extraordinary Ray (E-ray)

Light ray whose velocity depends on direction of propagation within a crystal. Follows a curved path.

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Wavefront

Imaginary surface connecting all points of a wave that are in the same phase; they are essentially 'slices' of a wave.

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Optic Axis

Line in a crystal defining the direction of light propagation where the two rays (O and E) have identical velocities.

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Normal Incidence

Light ray entering a crystal surface at 90 degrees; hence it enters perpendicular to the surface.

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Oblique Incidence

Light ray entering a crystal surface at an angle other than 90 degrees.

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Refractive Index

Ratio of the velocity of light in a vacuum to the velocity of light in a medium.

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Normal Incidence

Refracted wave fronts are parallel and travel together, creating a path difference between emerging waves, but no separation into distinct beams.

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Phase Difference (𝛿)

The difference in arrival time (or phase) between two waves after passing through different parts of a crystal.

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Extraordinary Ray Amplitude

The amplitude of the extraordinary ray in the crystal, calculated from the amplitude of incident plane polarized light and the angle it makes with the optic axis.

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Ordinary Ray Amplitude

The amplitude of the ordinary ray, calculated from the amplitude of incident plane polarized light and the angle it makes with the optic axis.

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Plane Polarized Light

Light with vibrations restricted to a specific plane.

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Optic Axis

The axis along which a crystal has uniform refractive properties.

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Equation for Extraordinary ray (x)

x = A cos θ.sin(ωt + δ)

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Equation for Ordinary ray (y)

y = A sin θ.sin ωt

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Elliptically polarized light

Light whose electric field vector traces an ellipse as it propagates.

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Plane polarized light

Light with vibrations confined to a single plane.

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Circularly polarized light

Light with vibrations forming a circle as it propagates.

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N-prism

Device used to detect polarization state by analyzing light's intensity changes during rotation.

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Quarter-wave plate

Optical component that introduces a phase difference of π/2 between ordinary and extraordinary rays.

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Babinet's compensator

Device for producing and analyzing elliptically polarized light, offering adjustable path differences.

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Intensity variation

Change in the strength of light when passing through a rotating polarizer.

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Quartz plate thickness for plane polarized light

The minimum thickness of a quartz plate required for the emergent light to be plane-polarized.

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Quartz plate thickness for circularly polarized light

The minimum thickness of a quartz plate required for the emergent light to be circularly polarized.

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Calcite plate for circularly polarized light

The minimum thickness of a calcite plate needed to convert plane polarized light into circularly polarized light.

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Optical path difference

The difference in the optical paths traveled by the ordinary and extraordinary rays in a crystal.

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Plate thickness from path difference

Calculating the thickness of a crystal plate given its optical path difference and the refractive indices of the ordinary and extraordinary rays.

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Rotation of polarization

The angle by which the plane of polarization rotates in a substance of a specific thickness for a given wavelength.

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Phase Difference

The difference in arrival time (or phase) of two waves after traversing different path lengths.

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Path Difference

The difference in the distances traveled by two waves.

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Phase Difference Equation

Phase difference = (2π/λ) x path difference

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Refractive Index Difference

The difference between refractive indices for left and right circularly polarized light in a substance.

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Specific Rotation (θ)

The angle of rotation of the plane of polarization for a given substance under particular conditions.

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Concentration (C)

The amount of substance dissolved per unit volume.

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Polarimeter Tube Length (l)

The length of the tube in which the sample is placed within the polarimeter.

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Specific Rotation (S)

A constant that relates the rotation angle to the concentration and path length of a substance in a polarimeter.

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Study Notes

Polarization of Light

  • Polarization is a property of waves, specifically light waves, indicating the direction of their oscillations
  • Light waves exhibit transverse nature, meaning vibrations are perpendicular to the direction of travel
  • Unpolarized light has vibrations in all directions, while polarized light has vibrations in a specific direction
  • Techniques for obtaining polarized light include reflection, refraction, double refraction, and selective absorption.

Double Refraction in Uniaxial Crystals

  • Uniaxial crystals have one optic axis, a line along which no double refraction occurs
  • These crystals, like calcite and quartz, transmit light as two rays: ordinary (obeying Snell's law) and extraordinary (not obeying Snell's law)
  • The ordinary ray's speed is constant in all directions, while the extraordinary ray's speed varies with the direction relative to the optic axis
  • The direction along which no double refraction takes place is called optic axis.

Positive and Negative Crystals

  • Positive crystals: The extraordinary ray travels slower than the ordinary ray
  • Negative crystals: The extraordinary ray travels faster than the ordinary ray

Principal Refractive Indices

  • In uniaxial crystals, two principal refractive indices exist: one for the ordinary ray (μo) and one for the extraordinary ray (μe)
  • μo represents the refractive index for the ordinary ray, which is the same in all directions
  • μe represents the refractive index for the extraordinary ray, which varies with the direction relative to the optic axis

Plane, Circularly, and Elliptically Polarized Light

  • Plane-polarized light vibrates in a single plane
  • Circularly-polarized light vibrates in a circle
  • Elliptically-polarized light vibrates in an ellipse

Quarter-Wave Plate

  • Used to convert plane-polarized light into circularly-polarized light
  • Introduces a phase difference of π/2 between ordinary and extraordinary rays

Half-Wave Plate

  • Used to convert plane-polarized light into plane-polarized light with the polarization plane rotated
  • Introduces a phase difference of π between ordinary and extraordinary rays

Babinet Compensator

  • An optical device for producing and analyzing elliptically polarized light
  • Allows for the introduction of variable phase differences between ordinary and extraordinary rays

Optical Activity

  • Certain substances (like sugar solutions) rotate the plane of polarization of light passing through them
  • Dextrorotatory substances rotate the plane of polarization clockwise, while levorotatory substances rotate the plane of polarization counterclockwise
  • Fresnal's explanation: optical rotation arises from the different speeds of right-handed and left-handed circularly polarized light

Specific Rotation

  • A measure of the degree of optical rotation for a given substance
  • Depends on the length and concentration of the solution, the wavelength of light, and temperature

Laurent's Half-shade Polarimeter

  • Used to measure the specific rotation of optically active substances
  • Uses a half-shade device to compensate for differences in light intensity, enabling precise measurements of rotation.

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