A converging lens of focal length 30 cm is placed in contact with another converging lens of unknown focal length, then possible value for focal length of combination is

Options

A. 15 cm
B. 60 cm
C. 36 cm
D. `-12cm`

Answer

To solve the problem of finding the possible value for the focal length of the combination of two converging lenses, we can follow these steps:

### Step 1: Understand the Lens Formula
We know that for two lenses in contact, the formula for the focal length \( f \) of the combination is given by:
\[ \frac{1}{f} = \frac{1}{f_1} + \frac{1}{f_2} \]
where \( f_1 \) is the focal length of the first lens and \( f_2 \) is the focal length of the second lens.

### Step 2: Identify Known Values
In this case, we have:
- \( f_1 = 30 \) cm (focal length of the first lens)
- \( f_2 \) is unknown.

### Step 3: Substitute Known Values into the Formula
Substituting the known value into the lens formula, we get:
\[ \frac{1}{f} = \frac{1}{30} + \frac{1}{f_2} \]

### Step 4: Analyze the Focal Lengths
Since both lenses are converging lenses, their focal lengths are positive. Therefore, \( f_2 > 0 \).

### Step 5: Determine the Range of Possible Values for \( f \)
From the equation, we can rearrange it to find \( f \):
\[ \frac{1}{f} = \frac{1}{30} + \frac{1}{f_2} \]
This implies:
\[ \frac{1}{f} > \frac{1}{30} \quad \text{(since \( \frac{1}{f_2} > 0 \))} \]
Thus:
\[ f < 30 \text{ cm} \]
This means the focal length of the combination is less than 30 cm.

### Step 6: Consider the Limits of \( f_2 \)
As \( f_2 \) approaches infinity (i.e., a very weak lens), \( f \) approaches 30 cm. Conversely, if \( f_2 \) is a very small positive value, \( f \) could be much smaller than 30 cm.

### Step 7: Conclusion
The possible value for the focal length of the combination must be a positive value less than 30 cm. Among the options provided, the only reasonable choice that fits this criterion is 15 cm.

### Final Answer
Thus, the possible value for the focal length of the combination is:
\[ \text{15 cm} \]