When a thin convex lens is put in contact with a thin concave lens of the same focal length (f), then the resultant combination has focal length equal to

Options

A. f/2
B. 2f
C. 0
D. `oo`

Explanation

To solve the problem of finding the focal length of a combination of a thin convex lens and a thin concave lens of the same focal length, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Focal Lengths**:
- Let the focal length of the convex lens be \( f_1 = +f \) (positive because it is a convex lens).
- Let the focal length of the concave lens be \( f_2 = -f \) (negative because it is a concave lens).

2. **Use the Formula for Focal Length of a Combination**:
- The formula for the effective focal length \( f_{effective} \) of two thin lenses in contact is given by:
\[ \frac{1}{f_{effective}} = \frac{1}{f_1} + \frac{1}{f_2} \]

3. **Substitute the Values**:
- Substitute \( f_1 \) and \( f_2 \) into the formula:
\[ \frac{1}{f_{effective}} = \frac{1}{+f} + \frac{1}{-f} \]

4. **Simplify the Expression**:
- This can be simplified as:
\[ \frac{1}{f_{effective}} = \frac{1}{f} - \frac{1}{f} = \frac{1 - 1}{f} = \frac{0}{f} = 0 \]

5. **Calculate the Effective Focal Length**:
- Since \( \frac{1}{f_{effective}} = 0 \), this implies:
\[ f_{effective} = \infty \]

### Final Answer:
The effective focal length of the combination of a thin convex lens and a thin concave lens of the same focal length is \( \infty \).