A ray of light is incident normally on the faces of the prism of apex angle 30° and refractive index √2 the angel of deviation of the ray is

To determine the angle of deviation for a ray of light incident normally on a prism with an apex angle of 30° and a refractive index of √2, we can use some fundamental principles of optics. Let’s break this down step by step.

Understanding the Basics

When light passes through a prism, it bends due to refraction. The amount of bending depends on the refractive index of the material and the angle at which the light enters the prism. In this case, the light is incident normally, which means it strikes the surface at a 90° angle.

Key Parameters

• Apex Angle (A): 30°
• Refractive Index (n): √2

Calculating the Angle of Deviation

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

D = nA - A

Where:

• D is the angle of deviation.
• n is the refractive index.
• A is the apex angle of the prism.

Substituting the Values

Now, let’s substitute the values into the formula:

D = (√2 * 30°) - 30°

First, we need to calculate √2 * 30°:

√2 is approximately 1.414, so:

√2 * 30° ≈ 1.414 * 30° ≈ 42.42°

Final Calculation

Now, substituting this back into the equation for D:

D = 42.42° - 30°

D ≈ 12.42°

Conclusion

The angle of deviation for the ray of light incident normally on the prism is approximately 12.42°. This result illustrates how the refractive index and the geometry of the prism influence the path of light as it travels through different media.

Understanding these concepts is crucial in optics, as they form the foundation for more complex phenomena such as total internal reflection and the design of optical instruments.