Two plane mirrors are positioned at 60° to each other. A ray of light strikes the first mirror at an angle of incidence of 40°. What is the angle of inciden...
Question 1 Report
Two plane mirrors are positioned at 60° to each other. A ray of light strikes the first mirror at an angle of incidence of 40°.
What is the angle of incidence when the reflected ray strikes the second mirror?
Answer Details
When light reflects off the first mirror, the angle of reflection equals the angle of incidence (40°), both measured from the normal to that mirror. The reflected ray then travels towards the second mirror. To find the angle of incidence on the second mirror, consider the geometry of the triangle formed by the two mirrors and the light path between them.
The angle between the two mirrors is 60°. Inside the triangle formed by the first mirror's normal, the reflected ray, and the second mirror, the angles must sum to 180°. The angle of reflection at the first mirror is 40°, so the angle between the reflected ray and the first mirror surface is \( 90° - 40° = 50° \). The interior angle at the point where the mirrors meet is \( 180° - 60° = 120° \) (or, more directly, the angle in the triangle at the junction is \( 60° \)). In the triangle: \( 50° + 60° + \theta_{\text{surface}} = 180° \), giving \( \theta_{\text{surface}} = 70° \). The angle of incidence at the second mirror is \( 90° - 70° = 20° \).
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