Understanding Image Formation by a Convex Lens When the Object is Between Focal Point and Optical Centre

The behavior of light rays and the resulting image formation within the context of a convex lens when the object is placed between the focal point and the optical center is a fundamental concept in optics. Understanding this phenomenon is crucial for various applications, from camera lenses to corrective eyewear.

Key Principles and Definitions

A convex lens, also known as a converging lens, is a type of lens that converges light rays that pass through it. The focal point, denoted as F, is the point where the light rays converge after passing through the lens. The optical center, O, is the midpoint of the lens through which the principal axis passes. When an object is placed between the focal point and the optical center, specific characteristics of the image formed come into play.

Characteristics of the Image Formed

When an object is placed between the optical center O and the focal point F of a convex lens, the following characteristics of the image are observed:

Location

The image is formed on the same side as the object, beyond the focal point F. This means that the light rays after passing through the lens appear to diverge and appear to originate from a point beyond the focal point. The image is positioned further away from the lens compared to the object.

Nature

The image is virtual. A virtual image is formed when light rays do not actually converge at a point, but rather appear to diverge after passing through the lens. This characteristic is due to the positioning of the object within the focal length of the lens.

Orientation

The image is upright. Unlike a real image formed by a convex lens when the object is beyond the focal point, or a virtual image formed when the object is beyond the focal point of a concave lens, the image formed in this case is upright. This means that the image appears in the same orientation as the object.

Size

The image is larger than the object. Since the object is within the focal length, the light rays coming from the object diverge after passing through the lens, resulting in a magnified image. The magnification is greater than 1, which means the image is enlarged compared to the object.

Summary of Image Characteristics

Image Type Nature Orientation Size Location Virtual Upright Enlarged On the same side as the object

Technical Explanation Using Lens Formula

To further understand the image formation, the lens formula can be utilized. The lens formula is given by:

1/f 1/v - 1/u

Where f is the focal length, v is the image distance, and u is the object distance. When the object is between the focal point and the optical center, the object distance, u, is less than the focal length, f. This means the absolute value of u is a number less than the absolute value of f. Using the lens formula and substituting the appropriate values, the image distance, v, can be calculated. The sign of v will indicate whether the image is real or virtual.

Inserting 0.5f for u and substituting into the lens formula provides:

1/v 1/f 1/u

Since u -0.5f (considering the sign convention where object distances are negative), the formula becomes:

1/v 1/f 1/(-0.5f)

1/v 1/f - 2/f

1/v -1/2f

v -2f

The negative sign of v indicates that the image is virtual. The image is also three times the size of the object, as the magnification (m) is given by:

m v/u

m -2f / (-0.5f)

m 4

Therefore, the image is four times larger than the object.

Visual Representation

For a visual understanding, consider the following diagram where the object is placed between the focal point and the optical center:

The viewer would be in the lower right corner of the diagram where the light rays are heading. It's evident that the image is further than the focal length and also larger than the object, which is 'magnified'. It's also upright, meaning the light rays reaching the viewer do not actually come from the image itself but from the object. This characteristic of a virtual image is clearly observed.

Case in point, the treatment of the light is such that the rays emanate as if they were diverging from a point beyond the object, which is an inherent property of virtual images.

Conclusion

The formation of a virtual, upright, and magnified image when an object is placed between the focal point and the optical center of a convex lens is a fascinating aspect of optics. Understanding this behavior is not only crucial for theoretical applications but also for practical use in various optical instruments.

Keywords

convex lens, image formation, virtual image, lens formula, image magnification