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

1. **Formula for Equivalent Focal Length**:
The formula for the equivalent focal length \( f_e \) of two lenses in contact is given by:
\[ \frac{1}{f_e} = \frac{1}{f_1} + \frac{1}{f_2} \]
where \( f_1 \) and \( f_2 \) are the focal lengths of the individual lenses.

2. **Identify the Focal Lengths**:
In this problem, we have:
- \( f_1 = 20 \, \text{cm} \) (for the first lens)
- \( f_2 = -20 \, \text{cm} \) (for the second lens)

3. **Substituting the Values**:
Now, substituting the values into the formula:
\[ \frac{1}{f_e} = \frac{1}{20} + \frac{1}{-20} \]

4. **Calculating the Right Side**:
Simplifying the right side:
\[ \frac{1}{f_e} = \frac{1}{20} - \frac{1}{20} = 0 \]

5. **Finding the Equivalent Focal Length**:
Since \( \frac{1}{f_e} = 0 \), we can conclude that:
\[ f_e = \infty \]

Thus, the equivalent focal length of the combination of these two lenses is infinity.

### Final Answer:
The equivalent focal length of the combination is \( \infty \).

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