Convex & Concave Lenses

Types of Lenses

Convex lenses are thicker in the middle and thinner at the edges. They are also called converging lenses because they cause parallel rays of light to converge (come together) to a point.

Concave lenses are thinner in the middle and thicker at the edges. They are also called diverging lenses because they cause parallel rays of light to spread out (diverge).

When light rays pass through a convex lens, they bend towards the principal axis and meet at the focal point. For a concave lens, the rays bend away from the principal axis as if they came from a focal point on the same side as the incoming light.

Image Formation by Convex Lenses

Convex lenses can produce both real and virtual images depending on the object's position relative to the lens's focal point.

Focal point (F) is the point where parallel rays of light converge after passing through the lens. The distance from the lens centre to the focal point is the focal length.

If the object is placed:

• Beyond 2F (twice the focal length): The image is real, inverted, smaller than the object, and formed between F and 2F on the opposite side.
• At 2F: The image is real, inverted, same size as the object, and formed at 2F on the opposite side.
• Between F and 2F: The image is real, inverted, larger than the object, and formed beyond 2F on the opposite side.
• At F: No image is formed because rays emerge parallel and never meet.
• Between the lens and F: The image is virtual, upright, larger than the object, and appears on the same side as the object.

Real images can be projected onto a screen, whereas virtual images cannot.

For example, a magnifying glass uses a convex lens to produce a virtual, enlarged image when the object is close to the lens.

For instance, if an object is placed 30 cm from a convex lens with a focal length of 10 cm (so between F and 2F), the image will be real, inverted, and magnified.

Image Formation by Concave Lenses

Concave lenses always produce virtual images. These images are:

• Upright (same orientation as the object)
• Smaller than the object
• Located on the same side of the lens as the object

This is because concave lenses cause light rays to diverge. The brain traces these rays back in straight lines, making the image appear to come from a point in front of the lens.

Concave lenses are also called diverging lenses because they spread out light rays.

For example, concave lenses are used in peepholes in doors to give a wide field of view with a smaller, upright image.

For instance, if parallel rays enter a concave lens, they diverge as if coming from the focal point on the same side as the incoming light.

Ray Diagrams for Lenses

Ray diagrams help to locate the image formed by lenses. The principal rays used differ for convex and concave lenses.

Principal Rays for Convex Lenses

• Ray 1: Parallel to the principal axis, refracts through the lens and passes through the focal point on the opposite side.
• Ray 2: Passes through the centre of the lens and continues straight without bending.
• Ray 3: Passes through the focal point on the object side, then refracts through the lens and emerges parallel to the principal axis.

The image is located where at least two refracted rays meet (real image) or appear to meet when extended backwards (virtual image).

Principal Rays for Concave Lenses

• Ray 1: Parallel to the principal axis, refracts through the lens and diverges as if coming from the focal point on the same side as the object.
• Ray 2: Passes through the centre of the lens and continues straight without bending.
• Ray 3: Directed towards the focal point on the opposite side, refracts through the lens and emerges parallel to the principal axis.

Since rays diverge, the image is found by extending the refracted rays backwards to where they appear to meet, forming a virtual image.

For example, drawing a ray diagram for a convex lens with an object beyond 2F shows the image formed between F and 2F, real and inverted.