5.32* A candle that is 6.00 cm tall is standing 10 cm from a thin con- ave lens whose focal length is -30 cm. Determine the location of the mage and describe it in detail. Draw an appropriate 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
![**Problem 5.32**
A candle that is 6.00 cm tall is standing 10 cm from a thin concave lens whose focal length is -30 cm. Determine the location of the image and describe it in detail. Draw an appropriate ray diagram.
### Solution Explanation
To find the image location and its properties, we will use the lens formula:
\[
\frac{1}{f} = \frac{1}{v} - \frac{1}{u}
\]
where:
- \( f \) is the focal length of the lens (-30 cm, since the lens is concave),
- \( v \) is the image distance,
- \( u \) is the object distance (-10 cm, since the object is on the same side as the light's origin).
Substituting the known values and solving for \( v \) will give the image distance.
### Ray Diagram
1. **Principal Axis**: Draw a horizontal line representing the principal axis.
2. **Lens**: Indicate the concave lens and mark the focal points on both sides of the lens.
3. **Object**: Place the object (candle) 10 cm from the lens on the principal axis.
4. **Ray 1 (Parallel Ray)**: Draw a ray parallel to the principal axis from the top of the object. After passing through the lens, this ray will diverge and appear to come from the focal point on the same side as the object.
5. **Ray 2 (Through Focal Point)**: Draw a ray from the top of the object through the focal point on the object side; after refraction, it becomes parallel to the principal axis on the opposite side.
6. **Ray Intersection**: The extension of these refracted rays will intersect on the object side, indicating the virtual image location.
### Image Characteristics
- **Type**: Virtual
- **Orientation**: Upright
- **Size**: Reduced (compared to the object)
This analysis helps in understanding the concept of image formation by concave lenses using ray diagrams.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0d7a912c-5a80-4a4e-9bd1-351936f105ca%2F5dfc7b55-53f9-4a61-8228-c0c35e0db3e2%2Fay3co8i_processed.png&w=3840&q=75)
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