By using a concave mirror, image of a tree is focused on a screen. The distance between the screen and the mirror is _____

Options

A. equal to radius of curvature of the mirror.
B. equal to half the radius of curvature of the spherical mirror.
C. equal to twice the focal length of the mirror.
D. equal to one fourth the focal length of the mirror.

Answer

To solve the question about the distance between the screen and the concave mirror when the image of a tree is focused on the screen, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Object Position**:
- The question states that the image of a tree is focused on a screen using a concave mirror. Since a tree is a large object located far away, we can consider it as being at infinity.

**Hint**: Remember that when an object is at infinity, the light rays coming from it are parallel.

2. **Behavior of Light Rays**:
- When parallel light rays from an object at infinity strike a concave mirror, they converge at the focus (F) of the mirror after reflection.

**Hint**: Think about how parallel rays behave when they hit a concave mirror.

3. **Image Formation**:
- For a concave mirror, when the object is at infinity, the image is formed at the focus (F). This is a key property of concave mirrors.

**Hint**: Recall the relationship between the object position and the image position for concave mirrors.

4. **Distance Between Screen and Mirror**:
- Since the image of the tree is formed at the focus, the distance between the screen (where the image is focused) and the mirror is equal to the focal length (f) of the mirror.

**Hint**: The screen must be placed at the location where the image is formed, which is the focus in this case.

5. **Relating Focal Length to Radius of Curvature**:
- The focal length (f) of a concave mirror is related to its radius of curvature (R) by the formula:
\[ f = \frac{R}{2} \]

**Hint**: Remember this relationship to understand the significance of the focal length in relation to the radius of curvature.

6. **Conclusion**:
- Therefore, the distance between the screen and the mirror is equal to the focal length (f) of the mirror.

### Final Answer:
The distance between the screen and the mirror is equal to the focal length (f) of the concave mirror.