Question

Determine the refractive index of the material of prism.

Hint:

Using a monochromatic light source is essential for this experiment as it produces a single, sharp spectral line (image of the slit), making accurate measurements of angles possible. If white light were used, the image would be a dispersed spectrum, and a clear angle of deviation could not be measured.

Answer 1

Step 1: Understanding the Concept:
The refractive index of a prism material can be determined accurately using a spectrometer. This method involves measuring two key angles: the angle of the prism (A), which is the angle between the two refracting faces, and the angle of minimum deviation (\(\delta_m\)), which is the smallest possible angle of deviation for light passing through the prism. These quantities are related by the prism formula.
Step 2: Key Formula and Apparatus:
Apparatus Required:
A spectrometer, a glass prism, a source of monochromatic light (e.g., a sodium vapour lamp), and a reading lens.
Key Formula:
The prism formula for refractive index is: \[ \mu = \frac{\sin\left(\frac{A + \delta_m}{2}\right)}{\sin\left(\frac{A}{2}\right)} \] Step 3: Detailed Procedure:
Part A: Measuring the Angle of the Prism (A)
1. Perform the initial adjustments of the spectrometer (leveling, focusing telescope and collimator).
2. Place the prism on the prism table with its refracting edge facing the collimator.
3. Turn the telescope to one side to receive the light reflected from one refracting face. Center the slit image on the vertical cross-wire. Record the reading from the vernier scale.
4. Turn the telescope to the other side to receive light reflected from the second refracting face. Again, center the slit and record the reading.
5. The difference between these two readings is equal to 2A. Thus, A can be calculated.
Part B: Measuring the Angle of Minimum Deviation (\(\delta_m\))
1. Place the prism on the table so that light from the collimator falls on one face and emerges from the other.
2. Locate the refracted image of the slit with the telescope.
3. Rotate the prism table slowly while observing the image. The image will move, reverse its direction, and move back. The position where it reverses direction is the position of minimum deviation.
4. Set the telescope cross-wire on the slit image at this turning point. Record the reading.
5. Remove the prism and move the telescope to view the direct image of the slit from the collimator. Record this reading.
6. The difference between the reading for the deviated ray and the direct ray gives the angle of minimum deviation, \(\delta_m\).
Step 4: Calculation:
Substitute the measured values of A and \(\delta_m\) into the prism formula to calculate the refractive index \(\mu\).