The angle of prism is 60°.When light is incident at an angle of 60° on the prism, angle of emergence is 40°. The angle of incidence I for which the light ray will deviate the least is such thatA) I60°

To determine the angle of incidence \( I \) for which the light ray will deviate the least when passing through a prism with an angle of 60°, we can apply some principles of optics, particularly Snell's Law and the concept of minimum deviation.

Understanding Prism Deviation

When light passes through a prism, it bends at both the entry and exit points. The angle of deviation \( D \) is defined as the angle between the direction of the incoming light and the direction of the outgoing light. The minimum deviation occurs when the light travels symmetrically through the prism.

Key Concepts

• Angle of Prism (A): This is the angle between the two faces of the prism. In this case, \( A = 60° \).
• Angle of Incidence (I): The angle at which light strikes the prism.
• Angle of Emergence (E): The angle at which light exits the prism. Here, \( E = 40° \).
• Minimum Deviation (D): The smallest angle of deviation occurs when the light enters and exits symmetrically.

Applying Snell's Law

Snell's Law states that \( n_1 \sin(I) = n_2 \sin(R) \), where \( n_1 \) and \( n_2 \) are the refractive indices of the media (air and prism, respectively), \( I \) is the angle of incidence, and \( R \) is the angle of refraction. For a prism, the relationship between the angles can be expressed as:

At minimum deviation, the angle of incidence \( I \) equals the angle of emergence \( E \). Therefore, we can denote:

Let \( I = E \) at minimum deviation.

Finding the Minimum Deviation Condition

Using the formula for the angle of deviation \( D \) in terms of the angle of incidence and the angle of prism:

\( D = I + E - A \)

Substituting \( E = I \) into the equation gives:

\( D = 2I - A \)

For minimum deviation, we can also express \( D \) as:

\( D = 60° - 40° = 20° \)

Solving for I

Now, substituting \( D \) back into the equation:

\( 20° = 2I - 60° \)

Rearranging gives:

\( 2I = 20° + 60° \)

\( 2I = 80° \)

\( I = 40° \)

Conclusion

Thus, the angle of incidence \( I \) for which the light ray will deviate the least is \( 40° \). This means that when light strikes the prism at this angle, it will experience the least deviation as it passes through the prism. Therefore, the correct answer to your question is that the angle of incidence \( I \) for minimum deviation is indeed \( 40° \).