|A child holds up a spoon 12 cm from her eye and looks into the concave surface that effectively has a focal length of 4.5 cm. She sees her image upside down. a) b) Where in front of the spoon does she see her image? What is its magnification? Is the image real or virtual?
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.
![### Physics Problem: Image Formation with a Concave Surface
**Problem Statement:**
A child holds up a spoon 12 cm from her eye and looks into the concave surface that effectively has a focal length of 4.5 cm. She sees her image upside down.
a) Where in front of the spoon does she see her image?
b) What is its magnification?
c) Is the image real or virtual?
**Solution Explanation:**
To solve these questions, we will use the mirror equation and magnification formula for concave mirrors.
1. **Mirror Equation:**
\[\frac{1}{f} = \frac{1}{d_o} + \frac{1}{d_i}\]
Here,
- \( f \) is the focal length
- \( d_o \) is the object distance
- \( d_i \) is the image distance
2. **Magnification Formula:**
\[M = -\frac{d_i}{d_o}\]
Here,
- \( M \) is the magnification
- \( d_i \) is the image distance
- \( d_o \) is the object distance
**Given Data:**
- Object distance, \( d_o = 12 \, \text{cm} \)
- Focal length, \( f = 4.5 \, \text{cm} \)
Plug these values into the mirror equation to find the image distance \( d_i \). Also, using the magnification formula, you can determine the magnification and nature of the image (real or virtual) based on the sign and value of \( d_i \).
**Note:** Since this problem involves a concave surface (mirror), follow the conventions for concave mirrors when applying these formulas.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc3275796-b029-439c-8f74-d618d19371ab%2F53ae4d58-7349-43b8-af32-7ff20cbbd34a%2Fkan76kc_processed.png&w=3840&q=75)
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