How to draw a graph between angle of incidence and deviation in ray when ray propagates from denser to rarer medium

To draw a graph that illustrates the relationship between the angle of incidence and the angle of deviation when a ray of light travels from a denser medium to a rarer medium, we first need to understand the underlying principles of refraction and how these angles interact. This concept is rooted in Snell's Law, which describes how light bends when it passes between different media.

Understanding the Basics

When light moves from a denser medium (like glass) to a rarer medium (like air), it bends away from the normal line. The angle of incidence (i) is the angle between the incoming ray and the normal, while the angle of refraction (r) is the angle between the refracted ray and the normal. The angle of deviation (D) is defined as the angle between the original path of the light and its new path after refraction.

Key Relationships

The relationship between these angles can be summarized as follows:

• Angle of Deviation (D): D = i - r
• Snell's Law: n1 * sin(i) = n2 * sin(r)

Steps to Draw the Graph

Now, let's break down the steps to create the graph:

1. Set Up Your Axes

Begin by drawing two perpendicular axes:

• The horizontal axis (x-axis) will represent the angle of incidence (i).
• The vertical axis (y-axis) will represent the angle of deviation (D).

2. Determine the Range of Angles

Choose a range for the angle of incidence. Typically, this could be from 0° to 90°. As the angle of incidence increases, observe how the angle of deviation changes.

3. Calculate Deviation Angles

Using Snell's Law, calculate the angle of refraction for various angles of incidence. For example, if you have a light ray moving from glass (n1 ≈ 1.5) to air (n2 ≈ 1.0), you can calculate the angles:

• For i = 0°, r = 0° (D = 0°)
• For i = 30°, use Snell's Law to find r, then calculate D.
• Continue this for several angles up to 90°.

4. Plot the Points

Once you have calculated the angles of deviation for various angles of incidence, plot these points on your graph. Each point corresponds to a specific angle of incidence and its resulting angle of deviation.

5. Connect the Dots

After plotting the points, connect them smoothly. You should notice that the graph typically shows a curve that starts at the origin (0,0) and rises as the angle of incidence increases, reflecting the increasing angle of deviation.

Interpreting the Graph

The resulting graph will illustrate that as the angle of incidence increases, the angle of deviation also increases, but not in a linear fashion. Initially, the increase in deviation is gradual, but as the angle of incidence approaches the critical angle, the deviation increases more sharply. This behavior is crucial in understanding optical phenomena such as total internal reflection.

Practical Example

Imagine shining a flashlight into a swimming pool. As the light enters the water (denser medium) at a shallow angle, it bends slightly. However, if you increase the angle, the light bends more dramatically. This visual can help you grasp how the angles interact and why the graph behaves as it does.

By following these steps, you can effectively create a graph that captures the relationship between the angle of incidence and the angle of deviation when light travels from a denser to a rarer medium. This understanding is fundamental in optics and helps in various applications, from designing lenses to understanding natural phenomena like rainbows.