a parralel beam of light falls normally on the first face of a prism of small angle.at d second face it is partly transmitted and partially reflected,the reflected beam striking at d first face again,and emergin from it in a direction making an angle 6^.30^'with d reversed direction....the refracted beam is found 2 have undergone a deviation of 1^.15^'from d original direction.Find d refractive index of d glass and d angle of prism....????

To solve this problem, we need to analyze the behavior of light as it passes through a prism, taking into account the angles of incidence, refraction, and reflection. Let's break down the situation step by step to find the refractive index of the glass and the angle of the prism.

Understanding the Geometry of the Prism

We have a prism with a small angle, and a parallel beam of light strikes the first face normally (at a 90-degree angle). When light hits the first face, it will pass through the prism without bending, since the angle of incidence is zero. However, when it reaches the second face, it encounters a different situation.

Refraction and Reflection at the Second Face

At the second face, the light beam is partially transmitted and partially reflected. The reflected beam then strikes the first face again. The key points to note here are:

• The angle of incidence at the second face will be equal to the angle of refraction at the first face, which is zero.
• The angle of deviation is given as 1.15 degrees from the original direction.
• The angle of the reflected beam makes an angle of 6.30 degrees with the reversed direction.

Calculating the Angles

Let’s denote the angle of the prism as A and the refractive index of the glass as n. The deviation (D) of the light beam can be expressed in terms of these variables. The total deviation can be calculated as follows:

Using the Deviation Formula

The deviation D for a prism can be expressed using the formula:

D = (n - 1)A

From the problem, we know that the total deviation is 1.15 degrees. Therefore, we can set up the equation:

1.15 = (n - 1)A

Finding the Angle of the Prism

Next, we need to relate the angle of reflection to the angle of the prism. The reflected beam makes an angle of 6.30 degrees with the reversed direction, which means it deviates by:

6.30 degrees = 2A (since the light reflects off the first face and then exits).

Thus, we can express A as:

A = 6.30 / 2 = 3.15 degrees.

Substituting Values to Find the Refractive Index

Now that we have A, we can substitute it back into the deviation equation:

1.15 = (n - 1)(3.15)

To isolate n, we rearrange the equation:

n - 1 = 1.15 / 3.15

n - 1 = 0.365

Therefore, n = 1 + 0.365 = 1.365.

Final Results

In conclusion, we have determined:

• The refractive index of the glass is approximately 1.365.
• The angle of the prism is 3.15 degrees.

This analysis illustrates how light interacts with a prism, demonstrating the principles of refraction and reflection, and how we can use these principles to derive important optical properties.