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.
Ray Optics
Optics is the study of light in the field of physics. It refers to the study and properties of light. Optical phenomena can be classified into three categories: ray optics, wave optics, and quantum optics. Geometrical optics, also known as ray optics, is an optics model that explains light propagation using rays. In an optical device, a ray is a direction along which light energy is transmitted from one point to another. Geometric optics assumes that waves (rays) move in straight lines before they reach a surface. When a ray collides with a surface, it can bounce back (reflect) or bend (refract), but it continues in a straight line. The laws of reflection and refraction are the fundamental laws of geometrical optics. Light is an electromagnetic wave with a wavelength that falls within the visible spectrum.
Converging Lens
Converging lens, also known as a convex lens, is thinner at the upper and lower edges and thicker at the center. The edges are curved outwards. This lens can converge a beam of parallel rays of light that is coming from outside and focus it on a point on the other side of the lens.
Plano-Convex Lens
To understand the topic well we will first break down the name of the topic, ‘Plano Convex lens’ into three separate words and look at them individually.
Lateral Magnification
In very simple terms, the same object can be viewed in enlarged versions of itself, which we call magnification. To rephrase, magnification is the ability to enlarge the image of an object without physically altering its dimensions and structure. This process is mainly done to get an even more detailed view of the object by scaling up the image. A lot of daily life examples for this can be the use of magnifying glasses, projectors, and microscopes in laboratories. This plays a vital role in the fields of research and development and to some extent even our daily lives; our daily activity of magnifying images and texts on our mobile screen for a better look is nothing other than magnification.
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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:**
In this task, you need to use two positive (converging) lenses to expand a laser beam. The beam starts off with a diameter of 1.0 mm and, after passing through the lens system, should emerge with a diameter of 8.0 mm. The given focal length of the first lens is 50.0 mm. With this information, you are to find:
1. The focal length of the second lens.
2. The distance separating the two lenses.
**Diagram:**
1. **Lens 1:** Represented by a convex lens with a focal length of 50.0 mm.
2. **Lens 2:** Another convex lens with an unknown focal length (which you need to find).
3. **Incoming Beam:** A thin line (or arrow) with a diameter label of 1.0 mm entering Lens 1.
4. **Expanding Beam:** A diverging line beyond Lens 1 that converges upon encountering Lens 2 and then diverges again, emerging with a diameter label of 8.0 mm after Lens 2.
5. **Separation (d):** The distance between Lens 1 and Lens 2 (to be calculated).
**Concepts to Use:**
- **Magnification in Optics:** The system expands the beam from 1.0 mm to 8.0 mm, representing a magnification (M) of 8.
- **Lens Formula and Magnification Relationship in an Optical System:** Use the relationships
\[
M = \frac{\text{Diameter of emerging beam}}{\text{Diameter of entering beam}}
\]
\[
M = \frac{f_2}{f_1}
\]
where \( f_1 \) and \( f_2 \) are the focal lengths of Lens 1 and Lens 2, respectively.
To solve, rearrange these equations to find \( f_2 \), and](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0d7a912c-5a80-4a4e-9bd1-351936f105ca%2F2e183be0-8463-46e2-9a3a-48222769f8cf%2Fmlxb6p_processed.png&w=3840&q=75)
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