Brief Summary
This lecture provides a comprehensive revision of light reflection and refraction, covering key topics such as plane mirrors, spherical mirrors, spherical lenses, refraction, and power. It begins with the corpuscular theory of light and rectilinear propagation, then moves into reflection, its laws, and image formation in plane and spherical mirrors. Refraction is explained with refractive index and its laws, followed by spherical lenses, image formation, lens formula, magnification, and power of lenses.
- Corpuscular theory of light and rectilinear propagation
- Reflection and its laws
- Image formation in plane and spherical mirrors
- Refraction, refractive index and its laws
- Spherical lenses, image formation, lens formula, magnification and power of lenses
Introduction
The lecture will cover reflection of light from various surfaces, including plane mirrors and surfaces, discussing the laws of reflection. It will then move on to spherical mirrors and their image formation, detailing concave and convex mirrors and how to calculate image and object distances. The lecture will also address refraction of light, explaining the bending of light as it moves from one medium to another due to changes in speed. Finally, it will cover spherical lenses, discussing how lenses form images, how light rays bend when passing through lenses, and lens formulas and power.
Corpuscular Theory of Light
In the 18th and 19th centuries, scientists like Newton studied the nature of light. Newton proposed the corpuscular theory, suggesting that light emerges from a source in the form of particles called corpuscles, indicating light has a particle nature. These particles are now known as photons. Experiments like solar cells, which operate on the photoelectric effect, support the particle theory of light.
Rectilinear Propagation of Light
Rectilinear propagation means light travels in a straight line. This is demonstrated by aligning three cardboards with holes in the centre. Light from a candle is visible when the holes are aligned, but if one cardboard is displaced, the light is blocked. This experiment proves light travels in a straight line, propagating from one place to another, like light from the sun reaching Earth.
How do we see ourselves in the mirror?
People see their images in mirrors every day, but the process involves reflection of light. A plane mirror forms an image of an object by reflecting light. The object is what we are looking at and the image is the representation formed in the mirror. The image is formed due to the reflection of light in the plane mirror.
Reflection of Light
Reflection of light is the phenomena of light bouncing back in the same medium. For example, if a light ray is incident on a plane mirror with air on one side and water on the other, the reflected ray will remain in the air, not enter the water. Every object reflects light, enabling us to see it.
Laws of Reflection
The laws of reflection govern how light reflects off surfaces. The first law states that the angle of incidence (I) is always equal to the angle of reflection (R). The second law states that the incident ray, the normal (a line drawn at 90 degrees to the surface at the point of incidence), and the reflected ray all lie in the same plane, meaning they move together like the wiper of a car.
Plane Mirror
In a plane mirror, the image and object are replicas of each other, copying each other's movements. The motion in the object is the same as the motion in the image. The image is literally inverted, meaning right appears as left and left appears as right. This is known as lateral inversion.
Characteristics of an Image formed by a plane mirror
The image formed by a plane mirror is always virtual and erect, meaning it appears behind the mirror and is upright. The size of the image is equal to the size of the object. The image is as far behind the mirror as the object is in front of it, meaning the object distance and image distance are the same. The image is also literally inverted, with right and left reversed.
Get to know about Spherical Mirrors
Spherical mirrors are used when magnification is needed, either to enlarge or reduce the image. These mirrors have a curved surface and can capture a complete field of view in a small mirror. The reflecting surface of a spherical mirror forms a part of a hollow sphere. The image size may or may not be equal to the object size.
Mirror Types
There are two types of spherical mirrors: concave and convex. A concave mirror has an inner reflecting surface, while a convex mirror has an outer reflecting surface. Concave mirrors are bulged inwards, like a cave, while convex mirrors are bulged outwards.
Terms related to the Spherical Mirror
Several terms are important when discussing spherical mirrors. Aperture is the diameter of the reflecting surface, with a larger aperture gathering more light for a brighter image. The centre of curvature is the centre of the sphere from which the mirror is formed, and the radius of curvature is the radius of that sphere. The principal axis is a straight line through the pole and centre of curvature. The principal focus is where parallel rays converge after reflection, and focal length is the distance between the focus and the pole. The pole is the centre of the reflecting surface.
Image Formation by Spherical Mirrors
To study image formation, it's important to know how to draw rays. There are three main rays to consider: a ray passing through the principal focus becomes parallel to the principal axis, or vice versa; a ray passing through the centre of curvature retraces its path because it is normal to the mirror; and a ray passing through the pole is reflected at the same angle, known as oblique incidence. For convex mirrors, rays parallel to the principal axis appear to come from the focus, and rays directed towards the centre of curvature retrace their path.
Cases of Image Formation by Concave mirror
When studying image formation, three parameters are considered: image size (same size, enlarged, or diminished), whether the image is real or virtual, and image and object distance. When the object is at infinity, the image is formed at the focus, is point-sized, and is real and inverted. When the object is beyond the centre of curvature, the image is between the focus and centre of curvature, is diminished, and is real and inverted. When the object is at the centre of curvature, the image is also at the centre of curvature, is the same size, and is real and inverted.
Uses of Spherical Mirrors
Concave mirrors are used by dentists to magnify images and in vehicle headlights to create a parallel beam of light by placing the bulb at the focus. Convex mirrors are used to get a wide field of view, such as in rear-view mirrors in vehicles.
Sign Conventions
Sign conventions are important for calculations involving mirrors. The pole of the mirror is taken as the origin of a Cartesian plane. Distances to the left of the pole are negative, to the right are positive, upwards are positive, and downwards are negative. Image and object heights also follow these conventions.
Mirror Formula and Magnification
The mirror formula, 1/f = 1/v + 1/u, relates image distance (v), object distance (u), and focal length (f). Magnification (m) is the ratio of image height (H') to object height (H), and is also equal to -v/u. All parameters must be entered with their correct signs. If magnification is positive, the image is virtual and erect; if negative, the image is real and inverted.
Refraction of Light
Refraction of light is the bending of light as it enters from one medium to another. This is why objects appear bent or broken when partially submerged in water. When light travels obliquely from one medium to another, the direction of propagation changes.
How does light ray gets Refracted on Glass Slab?
When light passes through a glass slab, it refracts twice. As light goes from air (rarer medium) to glass (denser medium), it bends towards the normal. As it exits from glass to air, it bends away from the normal. The emergent ray is displaced laterally from the incident ray. The angle of incidence is the angle between the incident ray and the normal, and the angle of emergence is the angle between the emergent ray and the normal.
What is Refractive Index?
Refractive index determines how much light bends when moving from one medium to another. It is the ratio of the speed of light in a vacuum (c) to the speed of light in a medium (v): n = c/v. A higher refractive index means the speed of light is slower in that medium. Diamond has the highest refractive index, meaning light travels slowest in diamond.
Laws of Refraction of Light
The first law of refraction states that the incident ray, the refracted ray, and the normal at the point of incidence all lie in the same plane. Snell's law states that the ratio of the sine of the angle of incidence to the sine of the angle of refraction is constant for a given pair of media: sin(i) / sin(r) = n2/n1, where n2/n1 is the refractive index of the second medium with respect to the first.
Get to know about Spherical Lenses
Lenses are transparent materials bounded by two surfaces. Convex lenses bulge outwards, while concave lenses curve inwards. Convex lenses are thick in the middle and thin at the edges, while concave lenses are thin in the middle and thick at the edges. Convex lenses converge light rays, while concave lenses diverge them.
Types of Spherical Lenses
Convex lenses are converging, meaning they bring light rays together. Concave lenses are diverging, meaning they spread light rays out.
Terms Related to the Spherical Lenses
Lenses have two spherical surfaces, each with a centre of curvature. The principal axis is an imaginary line passing through these centres. The optical centre is the central point of the lens. Aperture is the effective diameter of the lens, determining how much light it gathers. The principal focus is where parallel rays converge (convex) or appear to diverge from (concave). Focal length is the distance from the optical centre to the principal focus.
Image formation by Spherical lenses
To form images with lenses, certain rays are used. A ray passing through the principal focus or a parallel ray will pass through the principal focus after refraction. A ray passing through the optical centre does not deviate.
Image formation by Convex lenses
For convex lenses, when the object is at infinity, the image is formed at the focus, is point-sized, and is real and inverted. When the object is beyond C1, the image is between F2 and C2, is diminished, and is real and inverted. When the object is at C1, the image is at C2, is the same size, and is real and inverted. When the object is between C1 and F1, the image is beyond C2, is enlarged, and is real and inverted. When the object is at F1, the image is at infinity, and is highly enlarged. When the object is between F1 and O, the image is on the same side as the object, is enlarged, and is virtual and erect.
Image formation by Concave lenses
For concave lenses, when the object is at infinity, the image is at F1, is point-sized, and is virtual. When the object is anywhere between the optical centre and infinity, the image is between F1 and O, and is virtual, erect, and diminished.
Lens Formula and Magnification
The lens formula is 1/f = 1/v - 1/u, where f is focal length, v is image distance, and u is object distance. Magnification (m) is the ratio of image height to object height, and is also equal to v/u. Sign conventions are similar to mirrors. For concave lenses, focal length is negative; for convex lenses, it is positive. Object distance is always negative. If magnification is positive, the image is virtual; if negative, the image is real.
Power of lens
Power of a lens is its ability to converge or diverge light rays. A lens with more converging ability has more power and less focal length. Power is the reciprocal of focal length (P = 1/f), measured in diopters (D). For concave lenses, power is negative; for convex lenses, power is positive. Focal length must be in meters when calculating power. When combining lenses, the effective power is the sum of the individual powers.
