Introduction:
In this scenario, a plane mirror is revolving at a constant angular velocity of 2 revolutions per second (rps) about its normal. The mirror is placed at the center of curvature of a spherical screen with a radius of 10 meters. The light is incident from a fixed direction. We need to determine the velocity at which the light spot moves along the spherical screen.

Given:
- Angular velocity of the mirror: 2 rps
- Radius of the spherical screen: 10 meters

Calculating Linear Velocity:
To calculate the linear velocity of the light spot on the spherical screen, we can use the formula:

Linear velocity = angular velocity * radius

Here, the angular velocity is given as 2 rps and the radius of the spherical screen is 10 meters. Substituting these values into the formula:

Linear velocity = 2 rps * 10 meters = 20 meters per second

Therefore, the light spot moves along the spherical screen at a velocity of 20 meters per second.

Explanation:
When the plane mirror revolves about its normal, the incident light rays will be reflected at an angle equal to the incident angle. The angle of incidence is equal to the angle of reflection, as per the law of reflection.

Since the mirror is placed at the center of curvature of the spherical screen, all the reflected rays will converge at the center of curvature. As the mirror revolves, the reflected rays will form a circular path on the spherical screen.

The angular velocity of the mirror determines the speed at which the reflected rays move along the circular path. In this case, the angular velocity is given as 2 rps, meaning the mirror completes 2 revolutions per second.

By multiplying the angular velocity with the radius of the spherical screen, we can calculate the linear velocity of the light spot on the screen. This velocity represents the speed at which the light spot moves along the spherical screen.

In our calculation, the linear velocity is found to be 20 meters per second. This means that the light spot moves at a speed of 20 meters per second along the spherical screen.

Conclusion:
The light spot moves with a velocity of 20 meters per second along the spherical screen when the plane mirror revolves at a constant angular velocity of 2 rps about its normal. This motion is a result of the law of reflection and the convergence of reflected rays at the center of curvature of the screen.