Refractive Index of Prism Lab Manual

To determine the Refractive Index of the Material of a given Prism using Sodium Light

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1. Aim

To determine the refractive index of the material of a given prism using sodium light.

2. Apparatus Used

Spectrometer with vernier scale
Glass prism
Sodium vapor lamp (monochromatic light source)
Prism table
Reading lens
Magnifying glass
Spirit level
Clamps and stands

3. Diagram

$Experimental setup of spectrometer with prism for refractive index determination$

4. Theory

When a ray of light passes from one medium to another, its direction changes at the interface between the two media. This phenomenon is called refraction. The refractive index of a medium is a measure of how much the speed of light is reduced in that medium compared to its speed in vacuum.

The refractive index (n) of a medium is defined as the ratio of the speed of light in vacuum (c) to the speed of light in that medium (v):

\[ n = \frac{c}{v} \]

When light passes through a prism, it undergoes refraction twice: first when entering the prism and second when leaving it. The angle of deviation (δ) is the angle between the incident ray and the emergent ray.

For a prism, the angle of deviation (δ) depends on:

The angle of incidence (i)
The refractive index of the material (n)
The angle of the prism (A)

When the angle of deviation is minimum (δ_m), the ray passes through the prism symmetrically, which means the angles of incidence and emergence are equal. In this case, the refractive index can be calculated using the formula:

\[ n = \frac{\sin\left(\frac{A + \delta_m}{2}\right)}{\sin\left(\frac{A}{2}\right)} \]

where:

n = Refractive index of the prism material
A = Angle of the prism
δ_m = Angle of minimum deviation

5. Formula

\[ n = \frac{\sin\left(\frac{A + \delta_m}{2}\right)}{\sin\left(\frac{A}{2}\right)} \]

where:

n = Refractive index of the prism material
A = Angle of the prism
δ_m = Angle of minimum deviation

6. Procedure

I. Preliminary Adjustments of the Spectrometer:

Ensure the spectrometer is placed on a stable surface. Use a spirit level to check if the base is horizontal.

Loosen the telescope and rotate it. Focus the telescope for clear vision of distant objects by adjusting the eyepiece.

Fix the telescope in line with the collimator and adjust the collimator to obtain a sharp image of the slit.

Make sure the telescope and collimator are in the same horizontal plane.

II. Determination of the Angle of the Prism (A):

Place the prism on the prism table with its refracting edge (apex) facing the collimator.

Rotate the telescope to receive the light reflected from one face of the prism. Note the reading (R₁).

Rotate the telescope to receive the light reflected from the second face of the prism. Note the reading (R₂).

The angle of the prism is calculated using: A = 180° - |R₂ - R₁|.

III. Determination of the Angle of Minimum Deviation (δ_m):

Place the prism on the prism table with its refracting edge (apex) away from the collimator.

Rotate the prism table until the light from the collimator passes through the prism and enters the telescope.

Fix the prism table and rotate the telescope to observe the deviated image of the slit.

Slowly rotate the prism table while simultaneously moving the telescope to follow the deviated image. The image will first move in one direction, stop, and then move in the opposite direction.

When the image stops momentarily and changes direction, the prism is at the position of minimum deviation. Fix the telescope at this position and note the reading (D).

Remove the prism and rotate the telescope to directly observe the collimator slit. Note this direct reading (D₀).

The angle of minimum deviation is calculated as: δ_m = |D - D₀|.

IV. Calculation of Refractive Index:

Calculate the refractive index using the formula: \[ n = \frac{\sin\left(\frac{A + \delta_m}{2}\right)}{\sin\left(\frac{A}{2}\right)} \]

7. Observation Table

Table 1: For Determining the Angle of the Prism (A)

S.No.	Reading for first face reflection (R₁)	Reading for second face reflection (R₂)	Angle of the Prism (A = 180° - \|R₂ - R₁\|)
1.	____° ____'	____° ____'	____° ____'
2.	____° ____'	____° ____'	____° ____'
3.	____° ____'	____° ____'	____° ____'
Mean value of Angle of the Prism (A)			____° ____'

Table 2: For Determining the Angle of Minimum Deviation (δ_m)

S.No.	Direct reading (D₀)	Reading at minimum deviation (D)	Angle of Minimum Deviation (δ_m = \|D - D₀\|)
1.	____° ____'	____° ____'	____° ____'
2.	____° ____'	____° ____'	____° ____'
3.	____° ____'	____° ____'	____° ____'
Mean value of Angle of Minimum Deviation (δ_m)			____° ____'

8. Calculations

Given:

Mean angle of the prism (A) = ____° ____'
Mean angle of minimum deviation (δ_m) = ____° ____'

Converting to decimal degrees:

\[ A = \_\_\_\_° + \frac{\_\_\_\_'}{60} = \_\_\_\_° \] \[ \delta_m = \_\_\_\_° + \frac{\_\_\_\_'}{60} = \_\_\_\_° \]

Substituting in the formula:

\[ n = \frac{\sin\left(\frac{A + \delta_m}{2}\right)}{\sin\left(\frac{A}{2}\right)} \] \[ n = \frac{\sin\left(\frac{\_\_\_\_° + \_\_\_\_°}{2}\right)}{\sin\left(\frac{\_\_\_\_°}{2}\right)} \] \[ n = \frac{\sin(\_\_\_\_°)}{\sin(\_\_\_\_°)} \] \[ n = \frac{\_\_\_\_}{\_\_\_\_} = \_\_\_\_ \]

9. Result

The refractive index of the material of the given prism using sodium light (wavelength λ = 589.3 nm) is found to be:

\[ n = \_\_\_\_ \]

10. Precautions

Ensure that the spectrometer is properly leveled before beginning the experiment.
The slit of the collimator should be narrow and vertical.
The telescope and collimator should be properly focused to get sharp images.
The faces of the prism should be clean and free from dust or fingerprints.
The prism should be placed with its refracting edge (apex) exactly at the center of the prism table.
The base of the prism should be properly aligned with the prism table.
When determining the angle of minimum deviation, rotate the prism slowly to accurately identify the position where the deviation is minimum.
Take multiple readings and calculate the mean value to minimize random errors.
Ensure the room is dark enough to see the spectrum clearly.
Handle the optical components with care to avoid scratches or damage.

11. Viva Voice Questions

Q1: What is refraction of light?

Refraction of light is the phenomenon of change in the direction of light when it passes from one transparent medium to another. This change is due to the difference in the speed of light in different media.

Q2: Define refractive index. How is it related to the speed of light?

Refractive index (n) of a medium is defined as the ratio of the speed of light in vacuum (c) to the speed of light in that medium (v). Mathematically, n = c/v. It indicates how much light is slowed down in a medium compared to its speed in vacuum.

Q3: Why does minimum deviation occur in a prism?

Minimum deviation occurs when the ray of light passes through the prism symmetrically, meaning the angles of incidence and emergence are equal. At this position, the light ray travels parallel to the base of the prism inside it.

Q4: Why do we use sodium light in this experiment?

Sodium light is used because it is approximately monochromatic (single wavelength), which gives a sharp and clear image. This helps in precise measurements of angles. The wavelength of sodium D-line is 589.3 nm.

Q5: How does the angle of minimum deviation change with the wavelength of light?

As the wavelength of light increases, the angle of minimum deviation decreases. This is because the refractive index of a material generally decreases with increasing wavelength (normal dispersion).

Q6: What are the possible sources of error in this experiment?

Possible sources of error include improper focusing of the telescope or collimator, incorrect positioning of the prism, parallax error in reading the vernier scale, imprecise identification of the position of minimum deviation, and imperfections in the prism material.

Q7: What is dispersion of light?

Dispersion of light is the phenomenon where light of different wavelengths (colors) undergoes different amounts of refraction when passing through a medium. This causes white light to split into its component colors, as seen in a rainbow or when white light passes through a prism.

Q8: How does the refractive index of a material vary with temperature?

Generally, the refractive index of most materials decreases with increasing temperature because the density of the material decreases as it expands with heat.

Q9: What is the relationship between the angle of the prism and the angle of minimum deviation?

For small angles, the angle of minimum deviation is approximately equal to (n-1) times the angle of the prism, where n is the refractive index of the prism material.

Q10: Why is the spectrometer used for this experiment?

A spectrometer is used because it allows for precise measurements of angles (up to minutes and seconds), which is crucial for accurately determining the angle of the prism and the angle of minimum deviation.

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