What will be the angle of deviation for angle of incidence 35 degree, 40 degree, 45 degree, 50 degree, 55 degree, and 60 degree respectively for the primary colours i.e red, blue, yellow and a compound colour green,in a prism?

To determine the angle of deviation for various angles of incidence in a prism, we need to consider how light interacts with the prism material. The angle of deviation depends on the angle of incidence, the refractive index of the prism material, and the wavelength of the light, which varies for different colors. In this case, we will look at the primary colors red, blue, yellow, and the compound color green.

Understanding Refraction in a Prism

When light passes through a prism, it bends due to refraction. The amount of bending, or deviation, is influenced by the angle of incidence and the refractive index of the prism for different wavelengths of light. Each color has a different refractive index, which leads to varying angles of deviation.

Refractive Indices for Primary Colors

For our calculations, we can use approximate values for the refractive indices of the colors:

• Red: 1.620
• Yellow: 1.615
• Green: 1.610
• Blue: 1.590

Calculating Angle of Deviation

The angle of deviation (D) can be calculated using the formula:

D = (n - 1)A

Where:

• D: Angle of deviation
• n: Refractive index of the prism for the specific color
• A: Angle of the prism (which we will assume to be a constant value, typically around 60 degrees for these calculations)

Calculating for Each Angle of Incidence

Let’s assume the angle of the prism (A) is 60 degrees. We will calculate the angle of deviation for each angle of incidence (i) provided: 35°, 40°, 45°, 50°, 55°, and 60°.

Example Calculation for Red Light

For red light with a refractive index of 1.620:

• At 35°: D = (1.620 - 1) * 60 = 37.2°
• At 40°: D = (1.620 - 1) * 60 = 37.2°
• At 45°: D = (1.620 - 1) * 60 = 37.2°
• At 50°: D = (1.620 - 1) * 60 = 37.2°
• At 55°: D = (1.620 - 1) * 60 = 37.2°
• At 60°: D = (1.620 - 1) * 60 = 37.2°

Calculating for Other Colors

Using the same method, we can calculate for yellow, green, and blue:

• Yellow (1.615): D = (1.615 - 1) * 60 = 36.9°
• Green (1.610): D = (1.610 - 1) * 60 = 36.6°
• Blue (1.590): D = (1.590 - 1) * 60 = 35.4°

Summary of Results

Here’s a summary of the angles of deviation for each color at the specified angles of incidence:

• Red: 37.2°
• Yellow: 36.9°
• Green: 36.6°
• Blue: 35.4°

As you can see, the angle of deviation varies slightly for each color due to their different refractive indices. This phenomenon is what leads to the dispersion of light, creating a spectrum of colors when white light passes through a prism.