A parallel beam of monochromatic light falls on a combination of a convex lens and a concave lens of focal lengths 15 cm and 5 cm respectively. What is the distance between the two lenses to obtain a parallel beam of light from the concave lens ?

Options

A. 20cm
B. 3 cm
C. 10 cm
D. 45 cm

Answer

To solve the problem, we need to determine the distance between a convex lens and a concave lens such that a parallel beam of light emerges from the concave lens after passing through both lenses.

### Step-by-Step Solution:

1. **Identify the Focal Lengths:**
- The focal length of the convex lens (f₁) is +15 cm (positive because it converges light).
- The focal length of the concave lens (f₂) is -5 cm (negative because it diverges light).

2. **Understand the Lens Arrangement:**
- A parallel beam of light will converge to the focal point of the convex lens and then diverge from the concave lens. To achieve a parallel beam after the concave lens, the light rays must exit parallel to the original beam.

3. **Using the Lens Formula:**
- The lens formula is given by:
\[ \frac{1}{f} = \frac{1}{v} - \frac{1}{u} \]
- For the convex lens, we can consider the distance from the lens to the point where the rays converge (which will be at the focal length of the convex lens).

4. **Distance Calculation:**
- Let the distance between the two lenses be 'd'.
- The light rays converge at the focal point of the convex lens, which is at a distance of 15 cm from the convex lens.
- For the concave lens to produce a parallel beam, the light rays must be treated as coming from its focal point. Thus, the distance from the concave lens to the point where the rays converge should equal its focal length (5 cm).

5. **Setting Up the Equation:**
- The total distance from the convex lens to the concave lens plus the distance from the concave lens to the focal point (where the rays converge) should equal the focal length of the convex lens:
\[ d + 5 \text{ cm} = 15 \text{ cm} \]

6. **Solving for 'd':**
- Rearranging the equation gives:
\[ d = 15 \text{ cm} - 5 \text{ cm} = 10 \text{ cm} \]

### Final Answer:
The distance between the two lenses to obtain a parallel beam of light from the concave lens is **10 cm**.

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