12ª A meniscus concave glass (n₁ = 1.5) thin lens (see Fig. 5.12) has radii of curvature of +20.0 cm and +10.0 cm. If an object is placed 20.0 cm in front of the lens, show that the image distance will be - 13.3 cm. Describe that image and draw a ray 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.
How to solve this question
![**5.12** A meniscus concave glass (nₗ = 1.5) thin lens (see Fig. 5.12) has radii of curvature of +20.0 cm and +10.0 cm. If an object is placed 20.0 cm in front of the lens, show that the image distance will be -13.3 cm. Describe that image and draw a ray diagram.
**Explanation:**
1. **Lens Description**: The text describes a thin lens made of concave glass. The refractive index \( n_l \) is 1.5, which is common for glass materials.
2. **Radii of Curvature**: The lens has two surfaces with radii of curvature of +20.0 cm and +10.0 cm. These values indicate the curvature of the lens surfaces, essential for determining lens behavior using the Lensmaker's Equation.
3. **Lensmaker's Equation**: This equation is typically used to find the focal length \( f \) of a lens:
\[
\frac{1}{f} = (n - 1) \left(\frac{1}{R_1} - \frac{1}{R_2}\right)
\]
where \( n \) is the refractive index, \( R_1 \) and \( R_2 \) are the radii of curvature of the lens surfaces.
4. **Object Placement**: The object is placed 20.0 cm in front of the lens. This distance serves as the object distance (\( o \)) to be used in the lens formula.
5. **Image Distance**: The task is to determine that the image distance is -13.3 cm using the lens formula:
\[
\frac{1}{f} = \frac{1}{o} + \frac{1}{i}
\]
where \( o \) is the object distance, and \( i \) is the image distance.
6. **Ray Diagram**: A ray diagram should be drawn to visually represent the behavior of light rays through the lens, showing how the image distance is derived.
This exercise demonstrates the application of geometric optics principles, particularly how lenses form images and how mathematics can predict physical outcomes.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0d7a912c-5a80-4a4e-9bd1-351936f105ca%2F0b7b1daf-9c81-46b1-bf7b-63b275ba3ce6%2F5xi6vq6_processed.png&w=3840&q=75)
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