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VOOZH | about |
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VOOZH | about |
Ray Optics is the study of properties of light and optical instruments by assuming that light travels in a straight line. It is also known as geometrical optics, which deals with the geometry of light. Light always travels in a straight line, and the direction in which the light rays propagate is called the ray of light. It studies the principles and laws governing the propagation of light, particularly in the absence of wave effects such as interference and diffraction.
In this article, we will learn about ray optics, reflection, refraction, concave and convex mirrors, lenses, and formulas related to them.
Ray optics, also known as geometrical optics, is a branch of physics that studies the propagation of light by treating it as a collection of rays. These rays are essentially imaginary lines that represent the direction in which light travels. The form of energy that helps us see the objects around us is called light. The branch of physics that deals with the nature, properties, sources, and effects of light is called optics. Optics is broadly divided into two branches, namely physical optics, which is the study of the wave-like nature of light and the interactions between light and matter.
A mirror can be defined as an object that has a reflecting surface. When a light ray falls on a mirror, the incident ray, the reflected ray, and the normal to the surface of the mirror all lie in the same plane, and the angle of incidence is equal to the angle of reflection. Reflecting surfaces in mirrors obey laws of reflection. Let us read more about mirror and its types
Mirror as a reflecting surface can be classified as a plane mirror and spherical mirror.
Plane Mirrors are the those whose reflecting surface is plane. These are daily mirrors which just reflect image in their normal size and shape but laterally reversed. You can check out this with showing numbers on the mirror in your home, the number will always be reversed in mirror image.
Spherical Mirrors are those whose reflecting surface is curved. There are two types of spherical mirrors. These are
Concave Mirror are spherical mirror whose reflecting surface is curved in or bulge in. Consider the spoon with which you eat. That is what a concave mirror looks like. Concave mirrors are used shaving mirrors and in car head lights. They are converging in nature and generally produce magnified image.
You can read more about image formation in convex mirror.
Convex Mirror are spherical mirrors whose reflecting surface is curved out or bulge out. Consider the back side of a spoon. This represents a convex mirror. Convex mirror produces diminished images and are diverging in nature. They are used in car side mirrors.
Understand the difference between both concave and convex mirror here.
Some of the important terms related to mirror, are as follows.
Reflectionis the phenomenon where a wave (like light, sound, or water) bounces back from a surface. In the case of light, reflection allows us to see our image in mirrors, and it plays a crucial role in various optical applications. The light rays will get reflected from the polished surface.
There are two laws of reflection which are mentioned below:
The condition and nature of image formation in concave mirror is tabulated below:
| Object Position | Image Position | Nature of Image |
|---|---|---|
| At Infinity | The principal focus | Real, inverted and extremely diminished |
| Beyond the centre of curvature | Between the centre of curvature and focus | Real, inverted and diminished |
| At the centre of curvature | At the centre of curvature | Real, inverted object and image of the same size |
| Between focus and centre of curvature | Beyond the centre of curvature | Real, inverted, enlarged image |
| The principal focus | At Infinity | Extremely magnified |
| Between the pole and principal axis | Behind the mirror | Virtual, erect and magnified |
The condition and nature of image formation in convex mirror is tabulated below:
| Object Position | Image Position | Nature of Image |
|---|---|---|
| At Infinity | The principal focus | Virtual, erect and extremely diminished |
| Between infinity and pole | Appear between focus and pole | Virtual, erect and diminished |
The Mirror formula relates the object distance (u), image distance (v), and focal length (f) of a spherical mirror.
1/f = 1/u + 1/v
In the Mirror formula
These parameters u, v and f in mirror formula uses sign convention in mirrors and take sign accordingly.
The ratio of the height of the object to the height of the image is called linear magnification. (m) which describes the relative size of the image compared to the object. It can be calculated using two different formulations,
Ratio of image height to object height
m = hi/ho
In this formula
Ratio of image distance to object distance
m = - v/u
This formula relates magnification directly to the object and image distances through the mirror formula. The negative sign indicates that the image formed by a spherical mirror is typically inverted
Refractionis the phenomenon where a light changes direction as it travels from one medium to another with a different density. For light, this change in direction occurs because the speed of light varies in different materials.
There are two laws of refraction which are mentioned below:
Refractive index of a material is defined as the ratio of the speed of light in a vacuum (c) to the speed of light in the material (v). It describes how light propagates through a material. It is given as
n = c/v
where,
- n is refractive index
- c is speed of light in vacuum
- v is speed of light in medium
A lens is a transparent optical device that refracts or bends light rays when passes through it. It causes them to converge or diverge, and thus, forming images.
There are two major types of lens, concave lens and convex lens.
The condition and nature formed in convex lens is tabulated below:
| Object Position | Image Position | Nature of Image |
|---|---|---|
| At Infinity | At the focal point | Real, inverted and extremely diminished |
| Beyond 2F | Between F and 2F | Real, inverted and diminished |
| At 2F | At 2F | Real, inverted size of the image and object is the same |
| Between F and 2F | Beyond 2F | Real, inverted and bigger than the object |
| At the principal focus | At infinity | Real, inverted and extremely magnified |
| Between the optical centre and principal focus | Same side as the object | Virtual, erect and magnified |
The condition and nature of images formed by concave lens is tabulated below:
| Object Position | Image Position | Nature of Image |
|---|---|---|
| At Infinity | At the principal focus on the same side as the object | Virtual, erect and extremely diminished |
| Between infinity and pole | Appears between focus and pole | Virtual, erect and diminished |
The lens maker's formula is an equation used to relate the focal length (f) of a lens to its refractive index (n) and the radii of curvature (R1 and R2) of its two surfaces. It helps us understand how the shape and material of a lens affect its ability to focus light.
1/f = (n - 1)×(1/R1 - 1/R2)
where,
If the thickness of a lens is negligible in comparison to the radius of curvature, it is a thin lens. Thin lens formula is used to determine a relation between the focal length of the lens, the distance of the object, and the distance of the image. The lens formula is given as:
(1/f) = (1/v) - (1/u)
The parameters in above formula assume signs according to sign convention of lens.
Magnification of lens is the ratio of the height of the image produced and the height of the object. The magnification formula is given as
m = hi/ho = height of image/height of object
The another formula for magnification in terms of image and object distance is given as follows:
m = v/u = image distance/object distance
Power of a lens is a measure of its ability to bend light rays. It is measured in diopters. The formula states that the power of a lens is inversely proportional to its focal length.
P = 1/f
where
The SI unit of the power of the lens is m-1 or diopter.
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