The correct option for the question regarding the condition for minimum deviation in a glass prism is **D: the incident angle is equal to the angle of emergence**. Let's break down the reasoning behind this answer step-by-step. ### Explanation of the Correct Answer (Option D) 1. **Understanding Minimum Deviation**: - When a ray of light passes through a prism, it bends at the two surfaces of the prism due to refraction. The angle at which the light enters the prism is called the incident angle (i), and the angle at which it exits is called the emergence angle (e). - Minimum deviation occurs when the light ray passes symmetrically through the prism, meaning that the path of the light ray inside the prism is such that the angles of incidence and emergence are equal. 2. **Geometric Consideration**: - In the case of minimum deviation, the light ray enters the prism at an angle (i) and exits at the same angle (e). Therefore, at minimum deviation, we have: \[ i = e \] - This symmetry leads to the light ray being refracted at the same angle on both surfaces of the prism, which minimizes the overall deviation of the light ray. 3. **Prism Geometry**: - The prism has a specific angle, known as the apex angle (A). The relationship between the angles of incidence, refraction, and the apex angle can be described using Snell's Law and the geometry of the prism. - At minimum deviation, the angle of refraction (r) at the first surface and the angle of refraction at the second surface are also equal, leading to: \[ r_1 = r_2 \] - This condition is crucial for achieving minimum deviation. ### Why the Other Options are Incorrect - **Option A: Incident angle is equal to the angle of refraction**: - This statement is not generally true for refraction. The angle of incidence (i) and the angle of refraction (r) are related by Snell's Law: \[ n_1 \sin(i) = n_2 \sin(r) \] - They are equal only under specific conditions (like in air), but not in the context of a prism where the refractive indices differ. - **Option B: Refraction angle equals 90°**: - This is incorrect because a refraction angle of 90° would imply that the light ray is traveling along the boundary of the prism, which does not correspond to the condition of minimum deviation. Minimum deviation occurs when the light ray is refracted at angles less than 90°. - **Option C: Incident angle equals 90°**: - An incident angle of 90° means that the light ray is striking the surface of the prism perpendicularly. In this case, there would be no refraction occurring at the surface, as the light would continue straight through without bending. This does not lead to minimum deviation. ### Summary of Key Points - **Minimum Deviation Condition**: Occurs when the incident angle equals the angle of emergence (i = e). - **Symmetry in Refraction**: At minimum deviation, the angles of incidence and emergence are equal, leading to equal angles of refraction at both surfaces of the prism. - **Snell's Law**: The relationship between the angles of incidence and refraction is governed by Snell's Law, which is not satisfied by the incorrect options. - **Prism Geometry**: Understanding the geometry of the prism and the behavior of light as it passes through is crucial for solving problems related to refraction and deviation. This thorough understanding of the conditions for minimum deviation in a prism will help you tackle similar questions in your physics exams effectively.