Final answer:
The angle between the incident ray and the reflected ray at the plane mirror, given that the mirror is rotated through 200 revolutions, would be 144,000 degrees.
Step-by-step explanation:
To calculate the angle between a ray incident on the plane mirror and then reflected from it after the light has traveled to the curved mirror and back, we must consider the law of reflection and the fact that a plane mirror rotated through an angle θ will cause a reflected ray to deviate by an angle of 2θ. Since the plane mirror is rotated 200 revolutions, we convert this to degrees (1 revolution = 360 degrees), obtaining 200 × 360 degrees = 72000 degrees. There is no need to take into account the radius of curvature of the curved mirror as it does not affect the angle between the incident and reflected rays at the plane mirror. The final deviation angle of the ray is twice the rotation angle of the mirror, hence the angle between the incident and reflected ray would be 2 × 72000 degrees.