An isosceles prism of angle 120* has a refractive index 1.44.Two parallel monochromatic rays enter the prism parallel to each other as shown in figure.the ray emerge from the opposite faces-(A)Are parallel to each other(B)are diverging(C) make an angle 2[sin^ -1(0.72)-30*] with each other(D) make an angle 2 sin^ -1(0.72) with each otherCorrect answer is (C)Can someone please tell me how to solve this!I am attaching the link of the FIGURE too.. tyhttp://www.mediafire.com/?25boc7d2s7oal8u

To tackle the problem of the isosceles prism with an angle of 120 degrees and a refractive index of 1.44, we need to analyze how light behaves as it passes through the prism. The key here is to apply Snell's Law and understand the geometry of the situation. Let’s break it down step by step.

Understanding the Geometry of the Prism

An isosceles prism has two equal angles. In this case, the apex angle is 120 degrees, which means each base angle is 30 degrees (since 180 - 120 = 60, and 60/2 = 30). When light enters the prism, it will refract at both the entry and exit points.

Applying Snell's Law

Snell's Law states that n1 * sin(θ1) = n2 * sin(θ2), where:

• n1 is the refractive index of the medium the light is coming from (air, which is approximately 1.00).
• θ1 is the angle of incidence.
• n2 is the refractive index of the prism (1.44).
• θ2 is the angle of refraction inside the prism.

Calculating the Angle of Refraction

When the light enters the prism, it does so at an angle of 0 degrees (since it is parallel to the base). Therefore, the angle of incidence (θ1) is 0 degrees. Applying Snell's Law:

1.00 * sin(0) = 1.44 * sin(θ2)

This simplifies to:

0 = 1.44 * sin(θ2)

Thus, θ2 = 0 degrees. The light continues straight through the prism without bending at the first interface.

Refraction at the Exit Face

Now, as the light exits the prism, it will encounter the second interface. The angle of incidence at this point is 30 degrees (the angle of the prism). Applying Snell's Law again:

1.44 * sin(30) = 1.00 * sin(θ3)

Since sin(30) = 0.5, we have:

1.44 * 0.5 = sin(θ3)

Which gives:

sin(θ3) = 0.72

Now, we can find θ3:

θ3 = sin^(-1)(0.72)

Finding the Angle Between the Emerged Rays

When the two rays exit the prism, they will diverge. The angle between the two rays can be calculated as follows:

The total angle between the two rays after exiting the prism is:

Angle = 2 * θ3 = 2 * sin^(-1)(0.72)

This means the rays make an angle of 2 * sin^(-1)(0.72) with each other.

Conclusion

Thus, the correct answer is (C): the rays make an angle of 2 * sin^(-1)(0.72) with each other. This demonstrates how the geometry of the prism and the principles of refraction work together to determine the behavior of light as it passes through different media.

Approved