"Find prism material refractive index using a spectrometer"

Determine the refractive index of a prism using a spectrometer by measuring angles of minimum deviation and prism, ensuring precise alignment and readings.

Apparatus

Spectrometer, glass prism, and sodium lamp.

Theory

A spectrometer is an optical instrument used in laboratories to measure the wavelength of light and the refractive index of solids.
It mainly consists of three essential parts: Collimator, Prism Table, and Telescope.

Collimator

The collimator is a tube of adjustable length. It has a narrow slit S at one end and a convex lens L at the other. When light passes through the slit and the lens is properly adjusted, the collimator produces parallel rays of light.
This component ensures that light entering the prism is well-collimated and suitable for accurate measurements.

Prism Table

The prism table is a metallic platform equipped with leveling screws. A prism or grating can be placed on it. The table can rotate about a central axis and be fixed at any height.
It carries two vernier scales, V₁ and V₂, positioned opposite each other. As the prism table rotates, the verniers slide over a circular scale marked in degrees, helping measure the angles accurately.

Telescope

The telescope is used to view and measure the refracted or reflected rays. It contains a pair of cross-wires for observation.
It can rotate around the central axis of the prism table and lock in position. A fine-adjustment screw allows precise angular movement. The telescope’s position is read using the vernier scales V₁ and V₂.

Alignment and Adjustment of the Spectrometer

Before taking readings, follow these steps for proper alignment:

Focus the eyepiece on the cross-wires until they appear sharp.
Adjust the telescope for parallel rays by removing parallax between the image of a distant object and the cross-wires.
Set the collimator for a parallel light beam. Illuminate the slit using sodium or laser light and remove parallax between the slit image and the cross-wires.

These steps ensure that the optical axes of all parts are properly aligned.

Procedure

Adjust the spectrometer and switch on the sodium or laser light source.
Determine the vernier constant of the spectrometer.
Place the prism on the table so that its refracting edge is vertical and parallel to the slit. Adjust the collimator to illuminate both prism faces.
Keep the prism table fixed and rotate the telescope to receive reflected rays from face AB. Align the cross-wires to the image and note readings from both verniers (T₁).
Rotate the telescope again to receive reflected rays from face AC. Note the readings (T₂).
Repeat steps 4 and 5 at least three times.
Calculate the angle of the prism (A) as half of the angle between rays T₁ and T₂.
Next, place the prism so that the light passes through it and emerges from the other face. Rotate the table until the refracted image becomes stationary — this is the position of minimum deviation. Note both vernier readings (T₃).
Remove the prism and observe the direct image through the telescope. Record both readings (T₄).
The difference between these positions gives the angle of minimum deviation (Dₘ).
Take at least three sets of readings and calculate the refractive index (n) using the formula:

$\frac{\sin\left(\frac{A + D_m}{2}\right)}{\sin\left(\frac{A}{2}\right)}$

Observations and Calculations

Vernier constant of the spectrometer =………….

No. Of obs.	Vernier V₁			Vernier V₂
	Position of the telescope		Difference	Position of the telescope		Difference
	T₃	T₄	= T_{3 –}T₄	T₁	T₂	= T_{3 –}T₄
1. 2. 3.

Angle of the prism = A =
Mean value of = ………

No. of obs.	Vernier V₁			Vernier V₂
	Position of the telescope		Difference	Position of the telescope		Difference
	T₃	T₄	D_m = T_3- T₄	T₁	T₂	D_m = T_3- T₄
1. 2. 3.

Refractive index of the prism: Mean value of D_m = ……….

Precautions

Keep the slit width narrow for a sharp image.
Ensure that the telescope axis is perpendicular to the spectrometer’s vertical axis.
Keep the prism table fixed while measuring the prism angle.
If the vernier scale crosses zero while rotating the telescope, note this carefully during calculations.
Avoid parallax errors by adjusting the eyepiece and objective lens properly.
Handle the prism and instrument gently to avoid misalignment.

Result

The refractive index of the given prism material is found to be n = ………

“Find prism material refractive index using a spectrometer”