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 find the possible value for the focal length of the combination of two converging lenses placed in contact, we can follow these steps:

### Step 1: Understand the formula for the equivalent focal length of two lenses in contact.
The formula for the equivalent focal length (F_eq) of two lenses in contact is given by:
\[ \frac{1}{F_{eq}} = \frac{1}{F_1} + \frac{1}{F_2} \]
where \(F_1\) is the focal length of the first lens and \(F_2\) is the focal length of the second lens.

### Step 2: Assign values to the focal lengths.
In this case, we know:
- \(F_1 = 30 \, \text{cm}\) (the focal length of the first lens)
- \(F_2\) is unknown.

### Step 3: Substitute the known values into the formula.
Substituting the known value into the formula gives:
\[ \frac{1}{F_{eq}} = \frac{1}{30} + \frac{1}{F_2} \]

### Step 4: Rearrange the equation to find \(F_{eq}\).
To find \(F_{eq}\), we can rearrange the equation:
\[ \frac{1}{F_{eq}} = \frac{1}{30} + \frac{1}{F_2} \]
Taking the reciprocal gives:
\[ F_{eq} = \frac{30 \cdot F_2}{30 + F_2} \]

### Step 5: Analyze the limits of \(F_{eq}\).
- If \(F_2\) approaches infinity (very large), then:
\[ F_{eq} \approx 30 \, \text{cm} \]
- If \(F_2 = 0\) (a theoretical case), then:
\[ F_{eq} \approx 0 \, \text{cm} \]

### Step 6: Determine the range of possible values for \(F_{eq}\).
From the analysis, we conclude that the equivalent focal length \(F_{eq}\) can vary from \(0 \, \text{cm}\) to \(30 \, \text{cm}\).

### Step 7: Identify the possible value from the options.
Among the options provided, the only value that lies within the range of \(0 \, \text{cm}\) to \(30 \, \text{cm}\) is \(15 \, \text{cm}\).

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