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.
What is Ray Optics?
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.
What is Mirror?
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
Types of Mirror
Mirror as a reflecting surface can be classified as a plane mirror and spherical mirror.
- Plane Mirror
- Spherical Mirror
Plane 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 Mirror
Spherical Mirrors are those whose reflecting surface is curved. There are two types of spherical mirrors. These are
- Concave Mirror
- Convex Mirror
Concave Mirror
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
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.
Terms Related to Mirror
Some of the important terms related to mirror, are as follows.
- Pole: The centre point of the mirror through which the principal axis passes through the mirror is called the pole.
- Principal axis: The straight line that passes through the pole and the centre of curvature is called the principal axis.
- Centre of curvature: The centre of the sphere of which the mirror or lens is a part is called the centre of curvature.
- Radius of curvature: The radius of the sphere of which the mirror or the lens is a part is called the radius of curvature.
- Focal point or focus: It is a point at which all the rays parallel to principal axis meet after reflection.
- Focal length: The distance from the pole to the focal point is called the focal length.
Reflection and Laws of Reflection
Reflection is 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.
Laws of Reflection
There are two laws of reflection which are mentioned below:
- The incident ray, the reflected ray and the normal to the surface at the point of incidence all lie on the same plane.
- The angle of incidence will be equal to the angle of reflection.
Images Formed by Concave Mirror
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 |
Images Formed by Convex Mirror
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 |
Mirror Formula and Magnification
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
- u is the distance from the object to the mirror (positive when the object is in front of the mirror, negative when behind),
- v is the distance from the image to the mirror (positive the when the image is in front of the mirror, negative when behind).
- f is the Focal length of the mirror (positive for concave mirrors, negative for convex mirrors).
These parameters u, v and f in mirror formula uses sign convention in mirrors and take sign accordingly.
Magnification
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
- m is the Magnification (positive for enlarged images, negative for diminished images, and 1 for the same size),
- hi is the Height of the image
- ho is the Height of the object.
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
- If |m| < 1 then the size of the image is smaller than the object. The negative value of linear magnification shows that the image is real and inverted.
- If |m| > 1 then the size of the image is greater than the object.
Refraction and Laws of Refraction
Refraction is 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.
Laws of Refraction
There are two laws of refraction which are mentioned below:
- The incident ray, the refracted ray, and the normal to the interface at the point of incidence all lie in the same plane. This means all three elements are essentially coplanar, like objects placed on a flat surface.
- Snell’s Law: It states that the ratio of the sine of the angle of incidence to the sine of the angle of refraction is refractive constant. This constant is known as the refractive index of the second medium relative to the first.
Refractive Index
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
- The absolute refractive index of the medium is the ratio of the velocity of light in air or vacuum to that in the given medium. The velocity of light is maximum in a vacuum. The velocity in any other medium is less than the value in air. Thus, the absolute refractive index of the medium is always greater than unity.
Factors Affecting Refractive Index
- Refractive index of the medium depends on the nature and temperature of the medium. It also depends on the colour of the light ray.
- Refractive index is an optical property. Therefore, any impurity added to the medium will change the refractive index of the medium.
What is Lens
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.
Types of lens
There are two major types of lens, concave lens and convex lens.
Concave Lens
- It has refracting surface curved inwards.
- They are thinner in middle and thicker at the top and bottom.
- It produces smaller images.
- They can diverge a parallel beam of light.
Convex Lens
- It has outward curve refracting surface.
- It produces enlarged image.
- They are converging in nature.
- They are thicker in middle and thinner at top and bottom
Important Terms in a Lens
- Optical centre (C): The optical centre is the centre of the lens. The ray of light passing through the optical centre will not deviate.
- Principal axis: The line that passes through the centre of curvature and the optical centre is called the principal axis.
- Centre of curvature: The centre of the sphere of which the lens is a part is called the centre of curvature.
- Focal point or focus: The point on the principal axis where all the light rays will meet is known as the focal point.
- Focal length: The distance between the focus and the pole is called the focal length. The focal length is half of the radius of curvature.
Image Formed by 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 |
Image Formed by Concave Lens
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 |
Lens Maker Formula
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,
- f is the focal length of the lens (in meters)
- n is the refractive index of the lens material (a dimensionless quantity)
- R1 is the radius of curvature of the first surface (in meters) (positive for a convex surface, negative for a concave surface)
- R2 is the radius of curvature of the second surface (in meters) (positive for a convex surface, negative for a concave surface)
Lens Formula and Magnification
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)
- f = focal length of the lens
- v = distance of the image from the optical centre
- u = distance of the object from the optical centre
The parameters in above formula assume signs according to sign convention of lens.
Magnification 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
- If m > 1 then image is larger than object
- If m < 1 then image is smaller than object
- If m = 1 then image size is equal to object
Power of Lens
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
- P represents the power of the lens, measured in units of diopters (D).
- f represents the focal length of the lens, measured in units of meters (m).
The SI unit of the power of the lens is m-1 or diopter.
|
Related Articles |
|
|---|---|
Ray Optics Frequently Asked Questions
What is ray optics?
Ray optics also known as geometrical optics and it is a branch of optics that studies the behavior of light using the concept of rays.
What is the principle of Ray Optics ?
Ray Optics is based on the principle that Light travels in a straight lines in a uniform medium.
What are three branches of optics?
Three types of optics are Wave Optics, Geometric optics and Quantum optics.
What is angle of deviation?
The angle between the direction of incident ray and the emergent ray is called the angle of deviation
What are properties of light ?
The properties of light are Refraction, Reflection, Diffraction, Interference, Dispersion, Polarization and scattering.
What is u and v in rays optics?
In ray optics u is Object Distance and V is Image Distance measured from the pole or the optical center.
What is Snell’s law?
Snell’s law states that the ratio of sine of angle of incidence and angle of refraction is constant.