Light, Mirrors, and Lenses

Light is a form of energy that travels in a straight line.
Reflection of light is the bouncing back of a light ray when it strikes a smooth polished surface like a mirror.
Mirror is a shiny reflective surface that allows us to see our images due to the reflection of light.
Refraction of light is the change in direction of a light ray when it passes from one medium to another due to a change in traveling speed.
A straw in a glass appears bent due to refraction of light.
Lens is a transparent object used to study the refraction of light, with eyeglasses being an example.
Plain mirrors create virtual images that are laterally reversed and the same size as the object.
Spherical mirrors are curved mirrors with a reflective surface that forms part of a sphere.
Spherical mirrors have a pole, center of curvature, radius of curvature, and principal focus.
The relationship between the radius of curvature and focal length of a spherical mirror is R = 2f or F = R/2 for mirrors with a small aperture.
A convex mirror has an outward curved reflective surface, while a concave mirror has an inward curved reflective surface.
Refraction of light occurs due to a change in speed, causing a change in direction.
Refraction of light is observed in everyday life, such as a pencil appearing displaced in water or a lemon appearing bigger in a glass tumbler.
Snell's law of refraction states that the ratio of the sine of the angle of incidence to the sine of the angle of refraction is a constant for a given pair of media.
The refractive index of a medium measures how much the speed of light is reduced when it passes through that medium.
The speed of light is fastest in vacuum and slower in other media, with the refractive index being a measure of this reduction in speed.- Spherical lenses are transparent optical devices with spherical surfaces, which can be either convex or concave.
Convex lenses, also known as converging lenses, are thicker at the center and thinner at the edges, designed to converge or focus parallel incident light rays to a single point called the focal point.
Concave lenses, also known as diverging lenses, are thinner at the center and thicker at the edges, designed to cause parallel incident light rays to diverge away from the virtual focal point.
Each spherical surface forms part of a sphere, and the centers of these spheres are called the Centers of Curvature.
The imaginary straight line passing through the two centers of curvature of a lens is called the Principal Axis.
The optical center of a lens is the central point, a light ray passing through it will emerge undeviated for both types of spherical lenses.
An aperture is the effective diameter of the circular outline of a spherical lens.
Principal Focus (F) is the point where the rays parallel to the principal axis meet after refraction.
A lens has two spherical focal surfaces, and their distances from the optical center are called the focal lengths.
According to the rules for the ray diagram of spherical lenses:
- A ray that is parallel to the principal axis after refraction will pass through the principal axis in case of convex lenses and will appear to be coming from the principal focus in case of concave lenses.
- Light rays passing through a convex lens are directed towards the focus, while they will emerge parallel to the principal axis in case of concave lenses.
- A ray directed to the optical center emerges out undeviated for both types of lenses.
Image formation by convex lenses:
- If the object is at Infinity, the image position is at the focus FS2 and is highly diminished and point-sized, real, and inverted.
- If the object is beyond 2F1, the image position is between F2 and 2F2, the image is diminished, and the nature is real and inverted.
- If the object is at 2F1, the image position is at 2F2, the relative size is the same, and the image is real and inverted.
- If the object is at F1 and 2F1, the image position is beyond 2F2, the relative size is enlarged, and the image is real and inverted.
- If the object is at the focus F1, the image position is at Infinity, the relative size is infinitely large and highly enlarged, and the image is real and inverted.
- If the object is between the focus F1 and the optical center o, the image position is on the same side of the lens as the object, the relative size is enlarged, and the image is virtual and erect.
Image formation by concave lenses:
- If the object is at Infinity, the image position is at the focus F1, the relative size is highly diminished and point-sized, and the image is virtual and erect.
- If the object is between Infinity and the optical center o of the lens, the image position is between the focus and the optical center o, the relative size is diminished, and the image is virtual and direct.
Spherical lens Sign Convention: All measurements are taken from the optical center, and the focal length of a convex lens is positive, while that of a concave lens is negative.
Lens formula: 1/V - 1/U = 1/F, which gives the relationship between the object distance U and the image distance V and the focal length F.
Magnification M formula: M = h2/H, which measures how much the lens magnifies or reduces the size of an object as it forms an image.
Magnification M relationship: M = h2/H = V/U, where h is the height of the object, H is the height of the image, V is the image distance, and U is the object distance.
Power of lens: P = 1/F, which measures the ability of the lens to bend light and is represented by the letter P in units called diopters.
A lens with a positive power is called a converging lens, while a lens with a negative power is called a diverging lens.
Convex lenses have positive powers, while concave lenses have negative powers.