To solve the problem of finding the angle of incidence that will deviate a light ray by 120° through reflection from a plane mirror, we need to understand the relationship between the angle of incidence, the angle of reflection, and the total deviation of the light ray. ### Step-by-Step Explanation 1. **Understanding Deviation**: - Deviation is defined as the angle between the original path of the light ray and its final path after reflection. In this case, the engineer wants to deviate the light ray by 120°. 2. **Reflection Law**: - According to the law of reflection, the angle of incidence (i) is equal to the angle of reflection (r). This means that when a light ray strikes a mirror, the angle it makes with the normal (an imaginary line perpendicular to the surface at the point of incidence) is the same as the angle it makes with the normal after reflection. 3. **Calculating Total Deviation**: - The total deviation (D) can be expressed in terms of the angle of incidence and the angle of reflection: \[ D = i + r \] - Since \( r = i \) (from the law of reflection), we can rewrite the equation as: \[ D = i + i = 2i \] - Therefore, the total deviation is twice the angle of incidence. 4. **Setting Up the Equation**: - We know from the problem that the total deviation is 120°: \[ 2i = 120° \] 5. **Solving for the Angle of Incidence**: - To find the angle of incidence (i), we divide both sides of the equation by 2: \[ i = \frac{120°}{2} = 60° \] ### Conclusion The angle of incidence required to deviate the light ray by 120° through reflection from a plane mirror is **60°**. ### Evaluating the Options - **A. 60°**: This is the correct answer, as we calculated. - **B. 40°**: This would result in a total deviation of \( 2 \times 40° = 80° \), which is not sufficient to achieve the desired 120° deviation. - **C. 30°**: This would yield a total deviation of \( 2 \times 30° = 60° \), which is also not enough. - **D. 20°**: This would give a total deviation of \( 2 \times 20° = 40° \), far less than the required 120°. ### Summary - The angle of incidence is calculated using the relationship between incidence and reflection. - The total deviation is twice the angle of incidence. - For a total deviation of 120°, the angle of incidence must be 60°. - The other options do not satisfy the condition for the required deviation. This thorough understanding of the reflection principles and the calculations involved will help you tackle similar problems in the future.