A converging lens has a focal length of 0.12 m. To get an image of unit magnification the object should be placed at what distance from the converging lens ?

Options

A. 0.24 m
B. 0.12 m
C. 0.06 m
D. 0.4 m

Answer

To solve the problem, we need to find the distance at which the object should be placed from a converging lens to achieve unit magnification. Here's a step-by-step solution:

### Step 1: Understand Magnification
Magnification (m) is defined as the ratio of the height of the image (h') to the height of the object (h). For unit magnification, we have:
\[ m = \frac{h'}{h} = 1 \]
This means that the image height is equal to the object height, which also implies that the image distance (V) is equal to the object distance (U).

### Step 2: Use the Lens Formula
The lens formula relates the object distance (U), image distance (V), and focal length (F) of the lens:
\[ \frac{1}{V} + \frac{1}{U} = \frac{1}{F} \]

### Step 3: Substitute for Unit Magnification
Since we established that for unit magnification, \( V = U \). We can substitute V with U in the lens formula:
\[ \frac{1}{U} + \frac{1}{U} = \frac{1}{F} \]
This simplifies to:
\[ \frac{2}{U} = \frac{1}{F} \]

### Step 4: Solve for U
Rearranging the equation gives:
\[ U = 2F \]

### Step 5: Substitute the Given Focal Length
We are given that the focal length (F) of the lens is 0.12 m. Now we can substitute this value into the equation:
\[ U = 2 \times 0.12 \]
\[ U = 0.24 \, \text{m} \]

### Conclusion
The object should be placed at a distance of 0.24 meters from the converging lens to achieve unit magnification.

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