A converging lens has a focal length of x. An object, represented by the arrow, is placed at point A as seen in the figure here. A B D E Life The image of the object is most near which point? O (A) A O (B) B O (C) D O (D) E Need Help? Read It
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.
![### Understanding Converging Lenses in Optics
A converging lens, often referred to as a convex lens, has the ability to focus light onto a single point. The focal length of the lens, denoted as \( x \), is the distance from the center of the lens to the focal point where light rays converge.
#### Problem Description
In this educational exercise, you are tasked with determining the position where the image of an object will appear when placed in front of a converging lens.
**Scenario:**
- A converging lens with a focal length of \( x \) is illustrated.
- An object, represented by an arrow, is placed at point A. The distances from point A to the lens and other points are given in terms of the focal length \( x \).
**Diagram Explanation:**
The provided diagram shows a layout with a diverging lens and five specific points labeled as A, B, C, D, and E along the principal axis:
1. **Point A**: The starting position of the object, located at a distance \( x \) to the left of point B.
2. **Point B**: Located at a distance \( x \) to the left of the lens (C).
3. **Point C**: Center of the converging lens.
4. **Point D**: Located \( x \) to the right of the lens (C).
5. **Point E**: Located \( x \) to the right of point D.
#### Question:
The objective is to identify which point (A, B, C, D, or E) is closest to the location where the image of the object will form.
**Answer Options:**
- (A) A
- (B) B
- (C) D
- (D) E
#### Concept Insight:
To solve this, you need to apply the lens formula and properties of converging lenses:
\[ \frac{1}{f} = \frac{1}{d_o} + \frac{1}{d_i} \]
Where:
- \( f \) is the focal length.
- \( d_o \) is the object distance from the lens.
- \( d_i \) is the image distance from the lens.
For an object placed at a distance \( x \) (2x focal length) from the converging lens, the image forms at a distance \( x \) on the other side of the lens,](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe33ed983-9f3f-4edc-a3fb-37efbd4f1fcf%2F28064171-391c-4d62-b6a2-02fbf8035a6c%2Fwumgbqt_processed.png&w=3840&q=75)
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