Given Values and Problem Statement

Oct 13, 2025 by magicalceylontours.com 136 views

Convex lenses are a fundamental component in optics, used in various applications such as microscopes, telescopes, and cameras. The ability of a convex lens to focus light onto a specific point is crucial in understanding image formation. In this article, we will delve into the concept of image formation using a convex lens and explore the equation that governs this phenomenon.

The Convex Lens Equation

The convex lens equation is a mathematical formula that describes the relationship between the object distance (d0), the image distance (di), and the focal length (f) of a convex lens. The equation is given by:

d_i=\frac{d_0 f}{d_0-f}

This equation is a fundamental concept in optics and is used to calculate the image distance of an object placed at a specific distance from a convex lens.

Given Values and Problem Statement

In this problem, we are given the following values:

Object distance (d0) = 20.0 cm
Focal length (f) = 10.0 cm
Image distance (di) = ?

We are asked to find the image distance (di) using the convex lens equation.

Solving for Image Distance

To solve for the image distance (di), we can plug in the given values into the convex lens equation:

d_i=\frac{d_0 f}{d_0-f}

d_i=\frac{(20.0 \text{ cm})(10.0 \text{ cm})}{20.0 \text{ cm}-10.0 \text{ cm}}

d_i=\frac{200 \text{ cm}^2}{10 \text{ cm}}

d_i=20 \text{ cm}

However, we must consider the sign of the image distance. Since the image is formed on the same side of the lens as the object, the image distance is negative.

Conclusion

Therefore, the image distance (di) is:

d_i=-20.0 \text{ cm}

This result indicates that the image is formed 20.0 cm behind the lens, on the same side as the object.

Answer

The correct answer is:

B. -20.0 cm

Discussion

The convex lens equation is a powerful tool for understanding image formation in optics. By using this equation, we can calculate the image distance of an object placed at a specific distance from a convex lens. In this problem, we used the convex lens equation to find the image distance of an object placed 20.0 cm from a convex lens with a focal length of 10.0 cm. The result indicates that the image is formed 20.0 cm behind the lens, on the same side as the object.

Key Takeaways

The convex lens equation is a mathematical formula that describes the relationship between the object distance, image distance, and focal length of a convex lens.
The equation is given by: $$d_i=\frac{d_0 f}{d_0-f}$$
The image distance is negative when the image is formed on the same side of the lens as the object.
The convex lens equation is a fundamental concept in optics and is used to calculate the image distance of an object placed at a specific distance from a convex lens.

Applications of Convex Lenses

Convex lenses have numerous applications in various fields, including:

Microscopes: Convex lenses are used in microscopes to magnify small objects.
Telescopes: Convex lenses are used in telescopes to collect and focus light from distant objects.
Cameras: Convex lenses are used in cameras to focus light onto a sensor or film.
Optical instruments: Convex lenses are used in various optical instruments, such as binoculars and spectacles.

Conclusion

Frequently Asked Questions about Convex Lenses

Convex lenses are a fundamental component in optics, used in various applications such as microscopes, telescopes, and cameras. However, there are many questions and misconceptions about convex lenses. In this article, we will address some of the most frequently asked questions about convex lenses.

Q: What is a convex lens?

A: A convex lens is a type of lens that is thicker in the middle than at the edges. It is also known as a converging lens because it converges light rays to a single point.

Q: What is the purpose of a convex lens?

A: The purpose of a convex lens is to focus light onto a specific point. This is achieved by converging light rays to a single point, allowing us to see objects clearly.

Q: How does a convex lens work?

A: A convex lens works by refracting (bending) light rays as they pass through the lens. The light rays are bent towards the center of the lens, causing them to converge to a single point.

Q: What is the focal length of a convex lens?

A: The focal length of a convex lens is the distance between the lens and the point where the light rays converge. It is a measure of the lens's ability to focus light.

Q: What is the object distance of a convex lens?

A: The object distance of a convex lens is the distance between the lens and the object being viewed. It is a measure of how far away the object is from the lens.

Q: What is the image distance of a convex lens?

A: The image distance of a convex lens is the distance between the lens and the image formed by the lens. It is a measure of how far away the image is from the lens.

Q: How do I calculate the image distance of a convex lens?

A: To calculate the image distance of a convex lens, you can use the convex lens equation:

d_i=\frac{d_0 f}{d_0-f}

Where di is the image distance, d0 is the object distance, and f is the focal length.

Q: What is the difference between a convex lens and a concave lens?

A: A convex lens is thicker in the middle than at the edges, while a concave lens is thinner in the middle than at the edges. Convex lenses converge light rays to a single point, while concave lenses diverge light rays away from a single point.

Q: Can I use a convex lens to see objects that are far away?

A: Yes, you can use a convex lens to see objects that are far away. However, the lens must be powerful enough to focus the light from the object to a single point.

Q: Can I use a convex lens to see objects that are close up?

A: Yes, you can use a convex lens to see objects that are close up. However, the lens must be able to focus the light from the object to a single point.

Q: What are some common applications of convex lenses?

A: Some common applications of convex lenses include:

Microscopes: Convex lenses are used in microscopes to magnify small objects.
Telescopes: Convex lenses are used in telescopes to collect and focus light from distant objects.
Cameras: Convex lenses are used in cameras to focus light onto a sensor or film.
Optical instruments: Convex lenses are used in various optical instruments, such as binoculars and spectacles.

Conclusion

In conclusion, convex lenses are a fundamental component in optics, used in various applications such as microscopes, telescopes, and cameras. By understanding the basics of convex lenses, including their purpose, how they work, and how to calculate the image distance, you can use them to see objects clearly and accurately.