Two thin lenses of focal lengths 20 cm and -20 cm are placed in contact with other. The combination has a focal length equal to

Options

A. Infinite
B. 50 cm
C. 60 cm
D. 10 cm

Answer

To find the focal length of the combination of two thin lenses placed in contact, we can use the formula for the equivalent focal length of two lenses in contact:

\[ \frac{1}{f_{eq}} = \frac{1}{f_1} + \frac{1}{f_2} \]

### Step-by-Step Solution:

1. **Identify the Focal Lengths**:
- The first lens has a focal length \( f_1 = 20 \, \text{cm} \).
- The second lens has a focal length \( f_2 = -20 \, \text{cm} \).

2. **Substitute the Focal Lengths into the Formula**:
\[ \frac{1}{f_{eq}} = \frac{1}{20} + \frac{1}{-20} \]

3. **Calculate the Right Side**:
- The right side becomes:
\[ \frac{1}{20} - \frac{1}{20} = 0 \]

4. **Find the Equivalent Focal Length**:
- Since the sum is zero, we have:
\[ \frac{1}{f_{eq}} = 0 \]
- This implies:
\[ f_{eq} = \infty \]

5. **Interpret the Result**:
- An infinite focal length means that rays parallel to the optical axis will pass through the combination without converging or diverging. Thus, the combination behaves like a plane mirror.

### Conclusion:
The equivalent focal length of the combination of the two lenses is infinite.