Double Image Prism Experiment - Lab Manual

Determination of Refractive Indices for Ordinary and Extra-ordinary Rays

Double Image Prism Experiment

1 Aim

To determine the refractive indices for ordinary and extra-ordinary rays using a double image prism
(Wollaston Prism or Rochon prism).

2 Apparatus Used

Double Image Prism
(Wollaston or Rochon prism)
Spectrometer
With telescope and collimator
Sodium Lamp
Monochromatic light source
Reading Lens
For precise angle measurement
Spirit Level
For leveling the spectrometer
Adjustment Tools
Screwdrivers and Allen keys

3 Diagram

ordinary and extra ordinary rays

4 Theory

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Double Refraction (Birefringence):

When unpolarized light enters certain crystalline materials (like calcite or quartz), it splits into two refracted rays with different velocities and polarization states:

  • Ordinary Ray (O-ray): Follows Snell's law, has constant refractive index
  • Extra-ordinary Ray (E-ray): Does not strictly follow Snell's law, refractive index varies with direction

Double Image Prism:

A double image prism consists of two wedge-shaped pieces of birefringent crystal cemented together. The optic axes of the two pieces are oriented perpendicular to each other, causing the incident light to split into two images.

Refractive Index Relations:

For uniaxial crystals:

$n_o$ = refractive index for ordinary ray (constant)

$n_e$ = refractive index for extraordinary ray (variable)

Working Principle:

The double image prism separates the ordinary and extraordinary rays by a small angular deviation. By measuring the deviation angles and applying Snell's law, we can determine the refractive indices for both rays.

5 Formula

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Snell's Law Application:

$$n = \frac{\sin i}{\sin r}$$

Where: $i$ = angle of incidence, $r$ = angle of refraction

For Ordinary Ray:

$$n_o = \frac{\sin(A + \delta_m^o)}{\sin(A/2)}$$

For Extra-ordinary Ray:

$$n_e = \frac{\sin(A + \delta_m^e)}{\sin(A/2)}$$

Where:

$A$ = Apex angle of the prism

$\delta_m^o$ = Minimum deviation for ordinary ray

$\delta_m^e$ = Minimum deviation for extra-ordinary ray

$n_o$ = Refractive index of ordinary ray

$n_e$ = Refractive index of extra-ordinary ray

6 Procedure

1 Adjust the spectrometer for parallel rays by focusing the telescope for distant object and adjusting the collimator for parallel light.
2 Place the double image prism on the prism table and adjust it so that light from the collimator falls on one face of the prism.
3 Rotate the telescope to observe the emergent light. You should see two images (ordinary and extraordinary rays).
4 Identify the ordinary and extraordinary ray images based on their brightness and polarization properties.
5 For minimum deviation method, slowly rotate the prism table and observe both images until they reach minimum deviation position.
6 Record the positions of both images at minimum deviation for both ordinary and extraordinary rays.
7 Measure the apex angle of the prism using the spectrometer by the reflection method.
8 Calculate the minimum deviation angles for both rays and determine their respective refractive indices.

7 Observation Table

Table 1: Apex Angle Measurement

S.No. Position of Telescope Reflected Ray 1 (°) Reflected Ray 2 (°) Angle 2A (°) Apex Angle A (°)
1
2
3

Table 2: Minimum Deviation for Ordinary Ray

S.No. Direct Ray Position (°) Deviated Ray Position (°) Deviation δo (°) Refractive Index no
1
2
3

Table 3: Minimum Deviation for Extra-ordinary Ray

S.No. Direct Ray Position (°) Deviated Ray Position (°) Deviation δe (°) Refractive Index ne
1
2
3

8 Calculations

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Sample Calculation:

Given:

Apex angle: $A = $ ___ °

Minimum deviation for ordinary ray: $\delta_m^o = $ ___ °

Minimum deviation for extraordinary ray: $\delta_m^e = $ ___ °

For Ordinary Ray:

$$n_o = \frac{\sin\left(\frac{A + \delta_m^o}{2}\right)}{\sin\left(\frac{A}{2}\right)}$$

Substituting values:

$n_o = $ ___

For Extra-ordinary Ray:

$$n_e = \frac{\sin\left(\frac{A + \delta_m^e}{2}\right)}{\sin\left(\frac{A}{2}\right)}$$

Substituting values:

$n_e = $ ___

Average Values:

Mean refractive index for ordinary ray: $\bar{n_o} = $ ___

Mean refractive index for extraordinary ray: $\bar{n_e} = $ ___

9 Result

The refractive indices are:

Ordinary ray: $n_o = $ ___ ± ___

Extra-ordinary ray: $n_e = $ ___ ± ___

Birefringence: $\Delta n = |n_e - n_o| = $ ___

Conclusion: The double image prism successfully separates ordinary and extraordinary rays, demonstrating the birefringent properties of the crystal material.

10 Precautions

Handle the double image prism carefully to avoid scratches or damage to the optical surfaces.
Ensure the spectrometer is properly leveled before starting the experiment.
Use monochromatic light (sodium lamp) for accurate measurements.
Take readings only when the telescope crosshairs are clearly visible and focused.
Avoid parallax error while taking vernier readings.
Rotate the prism table slowly to find the exact minimum deviation position.
Keep the laboratory dark to improve visibility of the spectral lines.
Record multiple readings and take average values for better accuracy.

11 Viva Voice Questions

1. What is double refraction or birefringence?
Double refraction is the splitting of a light ray into two rays when it passes through certain crystalline materials. This occurs due to the anisotropic nature of the crystal, where light travels at different speeds in different directions.
2. What is the difference between ordinary and extraordinary rays?
Ordinary ray follows Snell's law and has a constant refractive index, while the extraordinary ray does not strictly follow Snell's law and its refractive index varies with the direction of propagation within the crystal.
3. How does a double image prism work?
A double image prism consists of two wedge-shaped pieces of birefringent crystal with their optic axes perpendicular to each other. This arrangement causes incident light to split into two differently polarized beams with different refractive indices.
4. What is the principle behind minimum deviation method?
The minimum deviation method is based on the principle that when light passes through a prism at minimum deviation, the ray inside the prism becomes parallel to the base of the prism, making calculations more accurate and simpler.
5. What are uniaxial and biaxial crystals?
Uniaxial crystals have one optic axis and show double refraction in all directions except along the optic axis. Biaxial crystals have two optic axes and more complex optical properties.
6. Why do we use monochromatic light in this experiment?
Monochromatic light is used to avoid dispersion effects and ensure that the refractive index measurements are for a specific wavelength, making the results more accurate and meaningful.
7. What is the significance of birefringence in practical applications?
Birefringence is used in polarizing filters, LCD displays, optical modulators, stress analysis in materials, and various optical instruments like polarimeters and wave plates.
8. How can you distinguish between ordinary and extraordinary rays?
Ordinary and extraordinary rays can be distinguished by their different intensities, polarization states, and deviation angles. Usually, one ray appears brighter than the other, and they have different polarization directions perpendicular to each other.
9. What is the optic axis of a crystal?
The optic axis is the direction in a crystal along which light can travel without experiencing double refraction. It is the direction along which ordinary and extraordinary rays have the same velocity.
10. What sources of error can affect this experiment?
Sources of error include: improper leveling of spectrometer, parallax errors in reading, non-monochromatic light, misalignment of optical components, temperature variations, and imperfections in the prism surfaces.
11. What is the role of polarization in double refraction?
In double refraction, the ordinary and extraordinary rays are linearly polarized in mutually perpendicular directions. This polarization difference is fundamental to the separation of the two rays.
12. How does temperature affect the refractive indices?
Temperature changes can alter the crystal structure and density, leading to variations in refractive indices. Generally, refractive indices decrease with increasing temperature for most materials.

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