Introduction
You might have heard that light has dual nature, it behaves boht as stream of particles and waves.
Well let's divide those 2 and learn.
In the scientific term we call stream of particles as "Geometrical optics" and wave like behaviour as "Physical optics".
Geometrical optics
Here in geometrical optics we assume light to be as rays or stream of particles. Although, there is a link between ray optics and wave optics. The theory connecting ray optics and wave optics is "Fermat's principle" also called the principle of least time or Fermat's principle of least time. It says, between any two points, light will take the quickest path not shortest. A path that can be traveled in the least time no matter if it's the longest. Both reflection and refraction follows Fermat's law. There are some rules/laws in both geometrical and physical optics. These laws are known after the Snell–Descartes law and ibn-Sahl law. For a reconstruction of this discovery see Hentschel 2001 . According to sources, it is now known that this law was already known to Ibn Sahl in 984. The same laws was also written by Ptolemy and during Middle Ages by Witelo, but due to lack of mathematical tools such as trigonometric functions their results were saved as tables, not functions. (Read history of optics to know more)
Snell's law's for reflection
1. Angle of incidence is always equal to the angle of reflection no matter how irregular the mirror is.
2. The incident ray, the reflected ray and the normal at the point of incidence, all lie in the same plane.
How do we see ?
Euclid postulated that visual rays proceed from the eyes onto objects and then we see them. It has something wrong in it because if visual rays proceed from our eyes then we would be able to see in dark. Actually we see objects when, beam of light falls on an object from the source of light, that light gets reflected in all directions. The reflected light then reaches our eye and brain interprets the object.
When 2 rays meet they form and image. A single ray cannot form an image. Real images are formed when rays actually intersect and forms an image but on the other hand virtual image is by extrapolating the rays and erect image is formed right-side up. Virtual images can't be captured on a screen but real images can be captured on screen. Real image are inverted and virtual images are erect.
Example for real image:- The movie we see in a cinema hall is a real image.
we are talking about light, glass objects such as mirror and prism helps us understand it even more better.
Spherical mirrors
A mirror who's surface is curved inwards is a concave mirror and who's surface is covered outwards is a convex mirror.
The centre of refracting surface of a spherical mirror is a point called pole. The pole is represented by the letter p. The reflecting surface of a spherical mirror forms us part of a sphere. This sphere has a centre the point is called centre of curvature. Centre of curvature is not the part of mirror. It lies outside its reflecting surface. It lies behind the mirror in case of a convex mirror. The line which passes through the pole and the centre of curvature is called the principal axis. The distance between the pole and the principal focus of a mirror is called focal length. It is denoted by the letter f and the distance between pole and the centre of curvature is called the radius of curvature. It is denoted by the letter R. However, there is a relationship between radius of curvature and focal length. R = 2f.
Modern mirrors may have many designs. In everyday life they mostly consist of a glass
plate coated with a thin layer of evaporated aluminium.
Concave mirror
These mirrors are used in vehicle headlights, torchlight, they are also used in shaving mirrors to get an enlarged view of face, even dentist use concave mirrors to see large image of patients teeth. Large concave mirrors are used to concentrate sunlight and produce heat in solar furnaces. Let's see some ray diagrams for image formation by a concave mirror.
The Chart below says how an image looks when it's kept in different positions.
Convex mirror
The mirror which you see on side of vehicle are convex mirrors. They are used as rear-view mirrors in vehicles. The most common reason why convex mirrors are perfect to use as rear view mirrors is because they always give virtual and erect image. Also the images diminished so they get a wider view. Let's see some ray diagrams for image formation by a convex mirror.
The Chart below says how an image looks when it's kept in different positions for a convex mirror.
Sign convention
Assuming pole P as the origin of the cartesian system. The principal axis can be taken as x-axis of the coordinate system. Hence, all the distance measured to right side of the origin is positive and to left side of the origin is negative. It's all same as cartesian system but instead of x-axis we are keeping principle axis.
Let's understand it with an example, by taking image formation of concave mirror at C.
Here, f is focal length and it's negative because the distance between pole and focus (F) comes under negative x-axis. U is distance between object and mirror and v is distance between image and mirror, both are negative because they come under negative x-axis, also hi (height of image) is negative for same reasons. But, the only one ho is positive because ho (height of object) comes under positive y-axis. Same goes with other ray diagrams for both concave and convex mirror.
Mirror formula:- 1/f = 1/v +1/u
Magnification
Magnification is because of which the image of an object is magnified with respect to object size.
Plane mirror
The mirror which you see on your dressing table is a plane mirror. Plane mirror forms the image of the object which is far from the mirror as the object. Hence, the distance between the object and the image from a plane mirror will always be in the ratio 1:1. For example, if you stand at a distance of 2 m from a plane mirror, then your image also forms 2 metres behind the mirror.
Plane mirror forms virtual and erect image. In plane mirrors image size is equal to object size. Plane mirrors form and lateral inverted image.
Ray diagram on how image forms in plane mirror
Refraction
Till now we said that light only travels in a straight line actually it's, light travels in a straight line untill it enters another medium. Mediums like air, water, glass etc. Its change of direction can be described by a single physical quantity, the "refractive index". It is higher in an optically ‘dense’ medium than in a ‘thinner’ one. Light speed in vacuum is 3×10⁸ m/s. This speed changes in different mediums because of which light rays bends when it enters another medium.
Different medium has their own refractive index. Thus, when a ray of light travelling from a rarer medium to a denser medium slows down and bends towards the normal. When it travels from a denser medium to a rarer medium, it speeds up and bends away from the normal.
Let's understand it with Example, suppose your travelling from your office to home and you see a path of sand crossing between the road. Now, what would happen if you enter the sand with the same speed with which you were travelling on concrete road. Yes, you will be pushed towards the normal. Here road is a rarer medium and sand is the denser medium. So, your car bends towards the normal. As shown in the picture below.
Another famous example was given by Richard Feynman, imagine Romeo discovering his great love Juliet at some distance from the shore of a shallow, a flowing river, she is struggling for her life in the water. Without thinking, romeo runs straight towards his goal – although he might have saved valuable time if he had taken the longer route, running the greater part of the distance on dry land, where he would have achieved a much higher speed than in the water.
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| Romeo takes the longest path (bc), which also decreases his speed because he is entering a denser medium (travelling through water for a long time), instead he could just walk through the sand (which is rarer compared to water) and then swim into denser medium for a short period of time which would save his time. |
Laws of refraction
1. The incident ray, the refracted ray and the normal at the point of incidence all lie in the same plane.
2. The ratio of angle, sign of incidence and sign of refraction is constant. These laws are called Snell’s law of refraction.
The constant value (n) is called the refractive index of second medium with respect to first medium.
If the medium one is air, then the refractive index of medium 2 is considered with respect to the first medium. It is represented as n2. If C is the speed of light in air and v is the speed of light in the given medium, then the refractive index of medium is;
where θ1 and θ2 are called the angle of incidence and angle of emergence at the interference.
Different material has different refractive index.
Total internal reflection
Critical angle:- When light is parallel to the medium then we say that light is at an critical angle.
Lenses
Lenses which are bulging outwords are double convex lens, simply called convex lens. Convex lens is thicker in the middle compared to its edges. The lens which you see in magnifying glass is a convex lens, as magnifying glass converges light rays coming from infinity into point size. So, convex lenses can be called as converging lenses. Similarly, spherical surfaces curved inwards and is thicker at the edges than in middle, is called a double concave lens. concave lens are used in telescopes, cameras, glasses and binoculars. It is also called a diverging lens.
The centre of this lenses (both concave and convex) is called centre of curvature. It is represented by the letter C. There are two centre of curvature in a lens, we can represent them as C1 and C2. The imaginary line which passes through centre of curvature is called a principal axis both in lenses and mirrors. The central point here is called optical centre. Represented as the letter O. When a ray of light passes through the optical centre it goes on without diverging/converging.
Some rules on how light behaves when passed from lenses:-
1. A ray of light parallel to principal axis after reflection with a convex lens, passes through the focus. But, with concave lens, the rays diverges, but when extrapolated, it passes through the focus.
2. A ray of light parallel to the principle access after reflection will still be parallel to principal axis for both concave and convex lenses.
3. When a ray of light passes through the optical centre it goes on without diverging/converging.
Convex lens
These lenses are widely used in eyeglasses to correct farsighted (Hyperopia). Let's see the position, size and nature of image of convex lens.
The Chart below says how an image looks when it's kept in different positions for a convex lens.
Concave lens
concave lens is used in telescopes, cameras, glasses and binoculars. It is also called a diverging lens. Let's see the position, size and nature of image of concave lens.
The Chart below says how an image looks when it's kept in different positions for concave lens.
( The cartesian co-ordinate system as it was in mirrors is also applied to lenses. )
Lens formula:- 1/f = 1/v - 1/u
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