Question

Draw graph between the angle of incidence and angle of deviation by using prism. Determine angle of minimum deviation (\(\delta_m\)).

Hint:

For best accuracy, use a sharp pencil for tracing rays and a protractor with clear markings. When aligning the pins, close one eye and ensure there is no parallax between them. The distance between the pins should be reasonably large (about 5-8 cm) to define the ray direction accurately.

Answer 1

Step 1: Understanding the Concept: 
When a ray of light passes through a prism, it undergoes refraction at two surfaces and deviates from its path. The angle of deviation (\(\delta\)) is the angle between the extended incident ray and the emergent ray. The value of \(\delta\) depends on the angle of incidence (i). As 'i' increases, \(\delta\) first decreases, attains a minimum value (\(\delta_m\)) at a specific angle of incidence, and then increases again. The plot of \(\delta\) versus i is a characteristic U-shaped curve. 
Step 2: Apparatus: 
Apparatus Required: 
A glass prism, a drawing board, white sheets of paper, drawing pins or tape, a protractor, a sharp pencil, and several all-pins. 
Step 3: Detailed Procedure: 
1. Setup: Fix a sheet of white paper on the drawing board. Place the prism on it and trace its triangular outline, label it ABC. 
2. Drawing Rays: - Draw a normal NN' to the face AB at a point P. 
- Draw an incident ray QP making an angle of incidence i (e.g., 35°) with the normal. 
- Fix two pins vertically on this incident ray. 
3. Locating Emergent Ray: Look for the images of these two pins through the other face AC. Fix two more pins, R and S, such that they appear to be in a straight line with the images of the first two pins. 
4. Measuring Deviation: - Remove the prism and pins. Join the points R and S to draw the emergent ray. 
- Extend the incident ray QP forward and the emergent ray RS backward. They meet at a point, and the angle between them is the angle of deviation \(\delta\). Measure this angle using a protractor. 
5. Repeating: Repeat the experiment for different values of the angle of incidence, such as 40°, 45°, 50°, 55°, and 60°, and measure the corresponding angle of deviation for each case. 
Step 4: Graph and Result: 
1. Plotting: Plot a graph with the angle of incidence (i) on the X-axis and the angle of deviation (\(\delta\)) on the Y-axis. 
2. Finding \(\delta_m\): The plotted points will form a smooth U-shaped curve. The lowest point on this curve corresponds to the angle of minimum deviation. 
3. Determining \(\delta_m\): Draw a horizontal tangent at the bottom of the curve. The point where this tangent touches the curve gives the value of \(\delta_m\) on the Y-axis. 
The result is stated as: "The angle of minimum deviation (\(\delta_m\)) from the graph is ..... degrees."