Two converging lenses of focal lengths `f_(1)=10cm` and `f_(2)=20cm` are placed at some separation. A parallel beam of light is incident on first lens. Then,

Options

A. for emergent beam form second lens to be parallel, the separation between the lenses has to be 30cm
B. for emergent beam from second lens to be parallel, the separation between the lenses has to be 60cm
C. if lenses are placed at such a separation that emergent beam from second lens is parallel, then the emergent beam width is 2cm if original beam has a width of 1cm
D. if lenses are placed at such a separation that emergent beam from second lens is parallel, then the emergent beam width is 4cm if original beam width is 1cm.

Explanation

To solve the problem, we need to determine the separation between the two converging lenses such that the emergent beam from the second lens is parallel to the incident beam on the first lens.

### Step 1: Understand the behavior of the lenses
When a parallel beam of light passes through a converging lens, it converges to a point known as the focal point. The position of the focal point depends on the focal length of the lens.

### Step 2: Analyze the first lens
Given:
- Focal length of the first lens, \( f_1 = 10 \, \text{cm} \)

When a parallel beam of light strikes the first lens, it will converge at its focal point, which is located at a distance of \( f_1 = 10 \, \text{cm} \) from the first lens.

### Step 3: Analyze the second lens
Given:
- Focal length of the second lens, \( f_2 = 20 \, \text{cm} \)

For the emergent beam from the second lens to be parallel, the light rays must converge at the focal point of the second lens. This means that the distance from the first lens to the second lens must be such that the light rays converge at the focal point of the second lens.

### Step 4: Set up the equation for the separation
Let \( d \) be the separation between the two lenses. The light rays converge at the focal point of the first lens, which is \( 10 \, \text{cm} \) from the first lens. For the rays to be parallel after passing through the second lens, they must reach the second lens at a distance equal to its focal length \( f_2 \).

Thus, the distance from the first lens to the second lens must be:
\[ d = f_1 + f_2 = 10 \, \text{cm} + 20 \, \text{cm} = 30 \, \text{cm} \]

### Step 5: Conclusion
Therefore, the separation between the two lenses must be \( 30 \, \text{cm} \) for the emergent beam from the second lens to be parallel.

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