The graph between angle of deviation (δ) and angle of incidence (i) for a triangular prism is a fundamental concept in optics. When light passes through a prism, it undergoes refraction at both surfaces, leading to deviation. The deviation depends on the angle of incidence, and the relationship is not linear.

Key characteristics of the δ vs i graph:

• The graph is a curve, not a straight line.
• It has a minimum point, known as the minimum deviation position. At this point, the angle of incidence equals the angle of emergence, and the light ray passes symmetrically through the prism.
• For angles of incidence less than and greater than that for minimum deviation, the deviation increases.
• The graph is symmetric about the vertical line through the minimum deviation point.

The deviation δ is given by the formula:

where $e$ is the angle of emergence and $A$ is the angle of the prism.

At minimum deviation (${\delta }_m$), the formula becomes:

and the refractive index $\mu$ is given by:

The correct graph is a smooth curve with a single minimum. It decreases to a minimum value and then increases again, forming a U-shaped curve (more precisely, a curve with one trough). Among the options, the graph that shows this behavior—starting high, decreasing to a minimum, and then increasing—is the correct representation.

Based on the typical shape, the second option (the one that appears like a curve with a clear minimum point) is correct. The images are not visible here, but the description matches the graph where δ first decreases and then increases with i.

Related Topics

Refraction through Prism: Understanding how light bends at the two surfaces of a prism and the resulting deviation.

Minimum Deviation: The condition under which the deviation is least, occurring when the path of light is symmetric inside the prism.

Dispersion of Light: Prisms are also used to disperse white light into its constituent colors, which is related to the variation of refractive index with wavelength.

Formulae

General deviation: $\delta =i+e-A$

At minimum deviation: ${\delta }_m=2i-A$ and $i=e$

Refractive index: $\mu =\frac{\sin \left[\frac{A+{\delta }_m}{2}\right]}{\sin \left(\frac{A}{2}\right)}$