1.A plane wavefront is incident on a concave mirror of radius ofcurvature R. The radius of the reflected wavefront will be :

1. Break Down the Problem

To solve the problem, we need to determine how a plane wavefront behaves when it reflects off a concave mirror, specifically calculating the radius of curvature of the reflected wavefront.

2. Relevant Concepts

1. A plane wavefront can be considered as having an infinite radius of curvature (R = ∞).
2. When a plane wavefront strikes a concave mirror, the law of reflection states that the angle of incidence is equal to the angle of reflection.
3. The relationship between the radius of curvature of the mirror and the radius of the reflected wavefront is given by the formula: $R' = \frac{R}{2}$ where $R'$ is the radius of curvature of the reflected wavefront and $R$ is the radius of curvature of the concave mirror.

3. Analysis and Detail

1. The incoming plane wavefront has a radius of curvature of $R = \infty$.
2. For the concave mirror, upon reflection, the outgoing wavefront will form a new spherical wavefront with its center located at the focal point of the mirror.

Using the formula: $R' = \frac{R}{2}$ we substitute $R$ for the radius of the mirror.

4. Verify and Summarize

Given that the radius of curvature $R$ is for a concave mirror, the radius of curvature for the reflected wavefront will also be calculated accordingly.

Final Answer

Thus, the radius of the reflected wavefront will be: $R' = \frac{R}{2}$