why does the graph of minimum deviation curve not touch the axes

The graph of the minimum deviation curve, often encountered in optics, particularly in the study of prisms, illustrates how light behaves as it passes through a prism at varying angles. One intriguing aspect of this graph is that it does not touch the axes, which can be a bit puzzling at first. Let’s break down the reasons behind this phenomenon.

Understanding Minimum Deviation

Minimum deviation occurs when light passes through a prism at a specific angle, resulting in the least bending of the light rays. This angle is crucial because it represents the most efficient path for light through the prism, minimizing the angle of deviation.

Graph Characteristics

The graph typically plots the angle of incidence on the x-axis against the angle of deviation on the y-axis. Here’s why the graph does not intersect the axes:

• Angle of Deviation Cannot Be Zero: When light enters a prism, it always deviates to some extent due to the change in medium. Therefore, the angle of deviation cannot be zero unless the light travels in a straight line without entering the prism, which is not the case in this context.
• Non-Negative Angles: Both the angle of incidence and the angle of deviation are always positive values in practical scenarios. The graph reflects this by remaining in the first quadrant, where both values are greater than zero.
• Minimum Deviation Point: The minimum deviation occurs at a specific angle of incidence, which is not at the origin. This point is where the graph reaches its lowest value of deviation, but it never actually touches the axes.

Visualizing the Concept

To visualize this, think of a car approaching a toll booth. The car can never be at the toll booth (zero deviation) unless it is not moving towards it at all. Similarly, light must interact with the prism to create deviation, so it cannot have an angle of deviation of zero while still entering the prism.

Practical Implications

This behavior of the graph has practical implications in optics. It helps in understanding how prisms can be used to disperse light into its constituent colors, as well as in designing optical instruments. By knowing that the graph does not touch the axes, scientists and engineers can better predict how light will behave in various applications.

In summary, the graph of the minimum deviation curve does not touch the axes because both the angle of incidence and the angle of deviation are always positive in the context of light passing through a prism. This characteristic is fundamental to understanding the behavior of light in optical systems.