5.50* Two positive lenses are to be used as a laserbeam expander. An axial 1.0-mm-diameter beam enters a short focal length positive lens, which is followed by a somewhat longer focal length positive lens from which it emerges with a diameter of 8.0 mm. Given that the first lens has a 50.0 mm focal length, determine the focal length of the second lens and the separation between the lenses. Draw a diagram.

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**5.50** Two positive lenses are to be used as a laser beam expander. An axial 1.0-mm-diameter beam enters a short focal length positive lens, which is followed by a somewhat longer focal length positive lens from which it emerges with a diameter of 8.0 mm. Given that the first lens has a 50.0 mm focal length, determine the focal length of the second lens and the separation between the lenses. Draw a diagram.

### Explanation:

This problem involves using two positive lenses to expand a laser beam from an initial diameter of 1.0 mm to a final diameter of 8.0 mm.

### Key Points to Consider:
- **First Lens**: This is a positive lens with a given focal length of 50.0 mm. It shortens the diverging rays, turning them into a more parallel beam or a slightly converging set of rays.
- **Second Lens**: This also needs to be a positive lens with a longer focal length. The objective is to determine this focal length so that the beam expands to the target diameter.

### Diagram: 
1. **First Lens**: Illustrate its effect by showing the incoming parallel rays (1.0 mm in diameter) converging or becoming less diverging after passing through the lens.

2. **Second Lens**: Positioned at a certain distance from the first lens. The distance should be calculated based on the optical properties and requirements of the system.

3. **Emerging Beam**: Show the beam expanding to a final diameter of 8.0 mm.

An optical ray diagram would visually represent how the rays enter, pass through, and emerge from the lens system. The lenses should be shown with their respective focal lengths, and the expansion of the beam should be demonstrated clearly.
Transcribed Image Text:**5.50** Two positive lenses are to be used as a laser beam expander. An axial 1.0-mm-diameter beam enters a short focal length positive lens, which is followed by a somewhat longer focal length positive lens from which it emerges with a diameter of 8.0 mm. Given that the first lens has a 50.0 mm focal length, determine the focal length of the second lens and the separation between the lenses. Draw a diagram. ### Explanation: This problem involves using two positive lenses to expand a laser beam from an initial diameter of 1.0 mm to a final diameter of 8.0 mm. ### Key Points to Consider: - **First Lens**: This is a positive lens with a given focal length of 50.0 mm. It shortens the diverging rays, turning them into a more parallel beam or a slightly converging set of rays. - **Second Lens**: This also needs to be a positive lens with a longer focal length. The objective is to determine this focal length so that the beam expands to the target diameter. ### Diagram: 1. **First Lens**: Illustrate its effect by showing the incoming parallel rays (1.0 mm in diameter) converging or becoming less diverging after passing through the lens. 2. **Second Lens**: Positioned at a certain distance from the first lens. The distance should be calculated based on the optical properties and requirements of the system. 3. **Emerging Beam**: Show the beam expanding to a final diameter of 8.0 mm. An optical ray diagram would visually represent how the rays enter, pass through, and emerge from the lens system. The lenses should be shown with their respective focal lengths, and the expansion of the beam should be demonstrated clearly.
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