For a concave mirror, paraxial rays are focused at distance `R/2` from pole and marginal rays are focused at distance x from pole, then (R is radius of curvature)

Options

A. `x=R/2`
B. `x = -f`
C. `xgtR/2`
D. `xltR/2`

Answer

To solve the problem, we need to analyze the behavior of paraxial and marginal rays in a concave mirror.

### Step-by-Step Solution:

1. **Understanding the Focus of a Concave Mirror**:
- The focal point (F) of a concave mirror is located at a distance of \( R/2 \) from the pole (P) of the mirror, where \( R \) is the radius of curvature.

2. **Identifying Paraxial Rays**:
- Paraxial rays are rays that are close to the principal axis and make small angles with it. For these rays, the focal point is at \( F = R/2 \).

3. **Identifying Marginal Rays**:
- Marginal rays are rays that are at the edge of the mirror and can be considered as rays that travel parallel to the principal axis. These rays converge at a different point compared to paraxial rays.

4. **Finding the Distance for Marginal Rays**:
- For a concave mirror, marginal rays focus at the same distance as the focal point but on the opposite side of the mirror. Therefore, if the focal point is at \( R/2 \) on the right side of the mirror, the marginal rays will focus at \( x = -F \).

5. **Substituting the Value of F**:
- Since \( F = R/2 \), we can substitute this into the equation for marginal rays:
\[ x = -F = -\frac{R}{2} \]

6. **Conclusion**:
- Thus, the distance \( x \) from the pole for marginal rays is given by:
\[ x = -\frac{R}{2} \]

### Final Answer:
The distance \( x \) from the pole for marginal rays is \( x = -\frac{R}{2} \).

---