at what distancefrom the bi-convex lens an object should be place such that an enlarged image is formed on the object itself (focal length of the lenses are written on the lenses)

To determine the distance from a bi-convex lens at which an object should be placed to form an enlarged image on the object itself, we need to consider the properties of lenses and the nature of image formation. A bi-convex lens, also known as a converging lens, can create real and virtual images depending on the position of the object relative to the lens's focal length.

Understanding Lens Basics

A bi-convex lens has two outward-curving surfaces, and its focal length (denoted as 'f') is the distance from the lens to the focal point, where parallel rays of light converge. The lens formula, which relates the object distance (denoted as 'u'), image distance (denoted as 'v'), and focal length, is given by:

1/f = 1/v - 1/u

Conditions for Enlarged Image

For an image to be enlarged and appear on the object itself, the object must be placed within the focal length of the lens. This scenario typically results in a virtual image, which is upright and larger than the object. The specific condition we are looking for is when the image distance 'v' equals the object distance 'u'. In this case, the image will be formed at the same location as the object.

Setting Up the Equation

Let’s denote the object distance as 'u' and the focal length as 'f'. Since we want the image distance 'v' to equal 'u', we can substitute 'v' in the lens formula:

1/f = 1/u - 1/u

This simplifies to:

1/f = 0

This indicates that the object must be placed at a distance less than the focal length of the lens. Therefore, the object distance 'u' must be:

• u < f

Practical Example

Suppose the focal length of the bi-convex lens is 10 cm. To achieve an enlarged image on the object itself, you would place the object at any distance less than 10 cm. For instance, if you place the object at 8 cm from the lens, the image formed will be virtual, enlarged, and located at the same position as the object.

Visualizing the Concept

Imagine holding a magnifying glass (which is essentially a bi-convex lens) close to a small object, like a coin. When you bring the lens closer than its focal length, the image of the coin appears larger and upright, allowing you to see more detail. This is the same principle at play when we discuss the placement of an object in relation to a bi-convex lens.

Summary of Key Points

• The object must be placed within the focal length of the lens to form an enlarged image.
• The distance from the lens should be less than the focal length (u < f).
• The image formed will be virtual, upright, and enlarged.

By understanding these principles, you can effectively manipulate the position of objects relative to lenses to achieve the desired image characteristics. If you have any further questions or need clarification on any point, feel free to ask!