Refraction of Light on Curved Surfaces - Key Notes
Convex Lens:
A convex lens is thicker at the center and thinner at the edges. When light rays pass through a convex lens, they converge or meet at a point known as the focal point.
The distance between the optical center of the lens and the focal point is called the focal length (f). Convex lenses are also known as converging lenses because they converge light rays.
They form real and inverted images of objects placed beyond the focal point.
Concave Lens:
A concave lens is thinner at the center and thicker at the edges. When light rays pass through a concave lens, they diverge or spread out.
The extension of diverging rays seems to originate from a point called the virtual focus or focal point.
Concave lenses are also known as diverging lenses because they diverge light rays. They form virtual and erect images of objects, which are always smaller than the actual object.
Sign Convention for Lenses:
The focal length (f) of a convex lens is positive (+f). The focal length (f) of a concave lens is negative (-f).
Distances measured in the direction of the incident light are considered positive, while distances measured opposite to the incident light are negative.
Lens Formula:
The lens formula is given as: 1/f = 1/v - 1/u, where f is the focal length, v is the image distance from the lens, and u is the object distance from the lens.
The positive sign for f indicates a convex lens, while the negative sign indicates a concave lens.
Magnification:
The magnification produced by a lens is given by the formula: magnification = height of image / height of object = v/u.
It can be positive (for real images) or negative (for virtual images). The magnification value greater than 1 indicates the image is larger than the object, while a value less than 1 indicates a smaller image.
Power of a Lens:
The power (P) of a lens is measured in Diopters (D) and is given by the formula: P = 1/f, where f is the focal length of the lens in meters.
Convex lenses have positive power, while concave lenses have negative power.
Image Formation with Convex Lens
1. Object at Infinity
When the object is at an infinite distance from the convex lens, the light rays coming from the object are practically parallel. The lens converges these parallel rays to a single point on the opposite side of the lens. As a result, a real and inverted image is formed at the focal point (F) of the lens. Example: When looking at a distant star through a convex lens, the image formed will be a real and inverted point-like image at the focal point of the lens.
2. Object Beyond 2F
When the object is located beyond twice the focal length (2F) of the lens, a real and inverted image is formed between the focal point (F) and the center of curvature (2F) on the opposite side of the lens. The image will be smaller in size than the object. Example: If the focal length of the lens is 20 cm, and the object is placed at a distance of 30 cm from the lens, the image will be real, inverted, and formed between 20 cm and 60 cm from the lens.
3. Object on 2F
When the object is placed exactly at twice the focal length (2F) of the lens, a real and inverted image is formed at the same distance on the opposite side of the lens. The image will be the same size as the object. Example: If the focal length of the lens is 15 cm, and the object is placed at a distance of 30 cm from the lens (center of curvature), the image will be real, inverted, and formed at a distance of 30 cm on the other side of the lens.
4. Between 2F and F
When the object is located between twice the focal length (2F) and the focal point (F) of the lens, a real and inverted image is formed beyond twice the focal length (2F). The image will be larger than the object. Example: Suppose the focal length of the lens is 10 cm, and the object is placed at a distance of 8 cm from the lens. In this case, the image will be real, inverted, and formed at a distance greater than 20 cm from the lens.
5. Object on F
When the object is placed exactly at the focal point (F) of the lens, the light rays become parallel after passing through the lens. As a result, no real image is formed. Instead, a virtual image is formed at infinity on the same side as the object. The virtual image will be magnified and upright. Example: If the focal length of the lens is 25 cm, and the object is placed at a distance of 25 cm from the lens, then the image will be virtual, upright, and formed at infinity on the same side as the object.
6. Object Between F and Optical Center
When the object is placed between the focal point (F) and the optical center of the lens, a virtual and upright image is formed on the same side as the object. The image will be larger than the object. Example: If the focal length of the lens is 12 cm, and the object is placed at a distance of 8 cm from the lens, then the image will be virtual, upright, and formed on the same side as the object.
Concave and Convex Lenses
Description
Simulation of image formation in concave and convex lenses.
Move the tip of the "Object" arrow to move the object. Move the point named " Focus' " to change the focal length.
Move the point named " Focus' " to the right side of the lens to change to a concave lens.