An object is kept at a distance more than twice the focal length (F) from a concave mirror. The distance the image formed will be

Options

A. less then F
B. equal to F
C. between F and 2F
D. More than 2 F

Explanation

To solve the problem of finding the distance at which an image is formed when an object is placed at a distance greater than twice the focal length (2F) from a concave mirror, we can follow these steps:

### Step 1: Understand the setup
- We have a concave mirror with a focal length (F).
- The radius of curvature (R) of the mirror is twice the focal length, i.e., R = 2F.
- The object is placed at a distance greater than 2F from the mirror.

### Step 2: Use the mirror formula
The mirror formula is given by:
\[ \frac{1}{f} = \frac{1}{u} + \frac{1}{v} \]
Where:
- \( f \) = focal length of the mirror
- \( u \) = object distance (taken as negative for concave mirrors)
- \( v \) = image distance (to be determined)

### Step 3: Assign values
Since the object is placed at a distance greater than 2F, we can say:
\[ u < -2F \]
For the focal length of a concave mirror, we have:
\[ f = -F \]

### Step 4: Substitute values into the mirror formula
Substituting the values into the mirror formula:
\[ \frac{1}{-F} = \frac{1}{u} + \frac{1}{v} \]
Rearranging gives:
\[ \frac{1}{v} = \frac{1}{-F} - \frac{1}{u} \]

### Step 5: Analyze the image distance
Since \( u \) is a large negative value (greater than -2F), the term \( \frac{1}{u} \) will be a small negative number. Thus, \( \frac{1}{-F} \) will dominate the equation, indicating that \( v \) will be negative, which means the image is formed on the same side as the object.

### Step 6: Determine the position of the image
When the object is placed beyond 2F, the image will be formed between F and 2F. This means that the image is real, inverted, and located between the focal point (F) and the center of curvature (2F).

### Conclusion
Thus, the distance at which the image is formed is between F and 2F.