Primary Colors

The colors that cannot be obtained by mixing any other colors in any proportions are called primary colors. The primary colors of light are red, green, and blue. These colors are also called basic colors of light. the reason for considering red, green and blue as primary colors is that all the other colors are made by mixing primary colors in suitable proportions. An interesting thing to be noted about primary colors is that when red, green and blue colors are mixed together they make white light.

Secondary Colors (Composite Colors)

The colors produced by mixing any two primary colors of light are called secondary colors or composite colors. Magenta, cyan and yellow colors are secondary colors.

Experiment for Formation of Secondary Colors

Take three torches and cover there glasses with red, green and blue cellophane papers, so as to produce red, green and blue light respectively. Now, switch on the torches and project all the three coloured lights on a white screen or wall, so that these coloured light may overlap. Now, you will observe that the area where red and green coloured lights overlap appears yellow. And the area where red and blue coloured lights overlap appears magenta. In the same way the area where blue and green coloured lights overlap gives cyan colour. Also, you will observe that the area where all the coloured lights overlap, appears white. We can also write these results as given below:

       Red      +      Green      =      Yellow

Red      +      Blue      =      Magenta

Blue      +      Green      =      Cyan

Complementary Colors

Complementary colors are the two colors, which give white light when mixed together. For example, red and cyan are complementary colors because they produce white light on mixing together. In the same way, blue and yellow, and green and magenta are also complementary colors. The complementary colors can be easily remembered with the help of figure given below. The colors present exactly opposite to each other in the triangle are complementary colors.

Colour Triangle to show formation of secondary colors from primary colors

The use of complementary colors is also common in our daily life. The best example of it is the mixing of indigo in lime during white washing of buildings. Actually, with the passage of time the colour of buildings becomes yellowish. Because blue colour is complementary colour of yellow colour so mixing of indigo in lime during white washing keeps the buildings white for a long time.

Pigments

The chemicals which imparts colour to other bodies are called pigments. For example, human blood is red in colour due to the presence of heamoglobin pigment in it. in the same way, the colour of most plants is green due to the presence of chlorophyll pigment.

Test Your Understanding and Answer These Questions:

1. What are primary colors? Give examples.
2. What are secondary colors? Give examples.
3. Give an experiment for the formation of secondary colors from primary colors.
4. What are composite colors? Give examples.
5. Why indigo is mixed in lime when a building is to be whitewashed?

We have already discussed that the white light is a mixture of seven different colors. When this white light consisting of seven colors falls on an object, then that object absorbs all the colors of the white light except one colour, which it reflects. And it is the colour of the reflected light which determines the colour of that object. For example, a rose (or blood) appears red in sunlight because when white light falls on rose (or blood), it absorbs all the colors of white light except red colour, which it reflects. This reflected red light by rose (or blood) enters our eyes and we feel the sensation of red colour. In the same way the leaves of plants appear green in sunlight because when white light falls on leaves, they reflects green colour to our eyes and absorbs all other colors. This reflected green light enters our eyes and we feel the sensation of green colour.

However, it is also observed that some objects absorb or reflect all the colors of white light which falls over them. If all the colors of white light are absorbed by an object, without reflecting any colour then such object appears black. For example, a black board appears black, because it absorbs all the colors of light falling on it. On the other hand, if all the colors of white light are reflected by an object without absorbing any colour then such object appears white. For example, the milk appears white because it reflects all the colour of white light falling on it.

Test Your Understanding and Answer These Questions:

1. Why do a rose appear red in color?
2. Why do leaves of plants appear green?
3. When does a body appear black?
4. When does a body appear white?
5. Why does milk appear white?

Recombination of spectrum colors means the combining together of seven colors of white light produced by a prism to give back the white light. This can be done by doing following experiment

Experiment to show recombination of colors

Take two glass prisms P1 and P2 and place the second prism P2 upside down with respect to the first prism P1. Now, allow a beam of white light to fall on first prism P1. The first prism splits the white light into seven colors. When these colors fall on the inverted prism, it recombines all the colors into white light which is observed ultimately as a patch of white light on the screen.

Test Your Understanding and Answer These Questions:

1. What do you understand by recombination of spectrum colors?
2. Give an experiment to show recombination of colors.

The dispersion of light is the phenomenon of splitting of a beam of white light into its seven constituent colours when passed through a transparent medium. It was discovered by Isaac Newton in 1666. Newton discovered that light is made up of seven different colours. He passed a beam of sunlight through a glass prism. The glass prism split the light into a band of seven colours on his wall. He called this band of colours the ‘spectrum’. Thus the spectrum is a band of seven colours which is obtained by splitting of white light by a glass prism. The order of colours from the lower end of spectrum is violet (V), indigo (I), blue (B), green (G), yellow (Y), orange (O), and red (R). The sequence of the 7 colours so obtained in a spectrum can be remembered by using the acronym ‘VIBGYOR’.

Cause of Dispersion of Light

The cause of dispersion of light is that white light consists of seven different colours, and each colour has different angle of deviation. Therefore, on passing through the prism different colours deviate through different angles. Hence the seven colours of white light separates and form a spectrum. Out of seven colours, the red colour deviates the least, and hence the red colour is present at the top of the spectrum. On the other hand, the violet colour deviates most that is why violet colour is present at the lower end of the spectrum.

Formation of Rainbow

The formation of rainbow is based on the process of dispersion of light. It is the most enchanting example of dispersion of light which takes place naturally. Usually a rainbow of seven colours is seen in the sky just after the rain when the Sun is shining. The essential condition to see the rainbow is that the observer must stand with his back towards the sun, when seeing the rainbow. Actually after the rain, a large number of water droplets remain suspended in the atmosphere. These droplets of water function as small prisms. So, when the white light emitted by Sun falls on these water droplets, then the white light is split into seven colours and rainbow is formed.

Test Your Understanding and Answer These Questions:

1. Define dispersion of light.
2. Who discovered the process of dispersion of light?
3. What is cause of dispersion of light?
4. What is spectrum?
5. Explain how a rainbow is formed?

The atmosphere of earth consists of different layers of air. Out of these some air layers are hot which have low densities, while the others are cold which have high densities. The hot layers of air behave as optically rarer medium for light rays, whereas the cold layers of air behave as optically denser medium for light rays. So, when an object emits light rays in the atmosphere, these light rays pass through the atmosphere having different air layers of different densities and get refracted by atmosphere. So, the refraction of light caused by the atmosphere of earth is called atmospheric refraction.

We will now discuss in detail some optical phenomenons which take place in nature due to the atmospheric refraction and total internal reflection of light.

Twinkling of Stars

The light rays coming from a star reaches our eyes after passing through the atmosphere having different air layers of different optical densities. But the optical densities of different layers of air keep on changing continuously due to change in temperature conditions. Due to which, the light rays coming from a star are refracted to different amount at different moments of time, and the path of refracted rays keep on changing. As a result, sometimes more light is refracted towards our eyes and the star appears bright to us, whereas sometimes less light is refracted towards our eyes and the star appears dim to us. This gives rise to the twinkling effect of a star.

The Sun is visible to us 2 minutes before actual sunrise and 2 minutes after the actual sunset

The Sun is visible to us 2 minutes before actual sunrise and 2 minutes after the actual sunset due to atmospheric refraction. Actually when the Sun is slightly below the horizon, then the light rays emitted by the Sun are refracted downwards when passing through the optically rarer air layers into the optically dense air layers of atmosphere. Due to which, the Sun appears to be slightly raised above the horizon and is visible 2 minutes before actual sunrise and 2 minutes after the actual sunset.

Mirage

Mirage is an optical illusion which occurs usually in deserts on hot summer days due to atmospheric refraction and total internal reflection of light rays. In mirage, the object such as a tree appears to be inverted as if it is situated on a bank of a pond of water. Actually on a hot summer day, the layers of air near the surface of earth become very hot and hence behave as optically rarer medium. On the other hand, the upper layers of air are comparatively cool and hence behave as optically denser medium. Now, a ray of light from the point T of a tree goes from denser to rarer medium along the path TB and bends away from the normal, at every layer due to atmospheric refraction. But at a particular layer, when the angle of incidence becomes greater than the critical angle, the total internal refraction occurs, and the totally reflected ray travels along the path BE and reaches the observer. Since, we can see the light rays only in straight line path, so the reflected ray BE appears to be coming from the point T’ to the observer. Due to this, an inverted image of the tree is formed below its actual position. And this inverted image of the tree creates the impression as if the reflection of tree is taking place from a pond full of water.

Looming

Looming is also an optical illusion which occurs usually in very cold regions. In looming, a distant object such as a ship moving in polar areas appears to be hanging in midair due to atmospheric refraction and the total internal reflection of light rays.

In Polar Regions the layers of air near the surface of earth are very cold and hence behave as optically denser medium. Whereas, the upper layers of air are comparatively warm and hence behave as optically rarer medium. Now, a ray of light coming from point S of ship goes from denser to rarer medium along the path SB and bends away from the normal, at every layer due to atmospheric refraction. But, at a particular layer, when the angle of incidence becomes greater than the critical angle, the total internal reflection occurs, and the totally reflected ray travels along the path BE and reaches the observer. As we have already discussed that we can see the light only in straight line path, so the reflected ray BE appears to be coming from the point S’ to the observer. Due to this, the observer sees a virtual and erect image of the ship at position S’, which is much above the actual position of the ship in the sea.

Brilliance of diamond

The brilliance of a diamond is due to the total internal reflection of light. We know that the refractive index of diamond is 2.42, and the critical angle for diamond is 24⁰. The diamond is cut in such a way so that the light which enters the diamond from any face suffers multiple total internal reflections at the various faces before coming out of the diamond. Due to this, the diamond sparkles.

Test Your Understanding and Answer These Questions:

1. What is atmospheric refraction?
2. Give an application of the process of total internal refraction.
3. Why do stars twinkle at night?
4. Explain why the Sun is visible to us 2 minutes before actual sunrise and 2 minutes after the actual sunset?
5. Define mirage? Explain mirage in hot areas with the help of a diagram.
6. What is looming? Explain looming with the help of a diagram.
7. What is the reason of brilliance of diamond?

Total internal reflection is a very interesting phenomenon which takes place when light rays pass from an optically denser medium (e.g. water, glass) into optically rarer medium (e.g. air). Now, we shall discuss the concept of total internal reflection by taking three different cases. These are:

Case 1

Consider a point object O is placed in a tank full of water. Now, a ray of light OA starting from the point object O, bends away from the normal AN along the direction AB in the air. As the refracted ray AB is going away from the normal so the angle of refraction r is greater than the angle of incidence i.

Case 2

Now, as we increase the angle of incidence i, the angle of refraction r also increase. By increasing the angle of incidence up to a particular value which is called the critical angle (i = c), the angle of refraction r becomes equal to 900, and the refracted ray don’t go into air but gores along the horizontal water surface in the direction CD. So, critical angle may be defined as the angle of incidence in the denser medium for which the angle of refraction in rarer medium is 900. The critical angle is represented by letter ‘c’.

The value of critical angle for different substances is different, as given in table

Table of Critical Angle of different substances

Case 3

Now, if the angle of incidence i is greater than the critical angle (i.e. i > c) then the ray of light OE is reflected back into the water along the direction EF, without going into the air. This phenomenon is called total internal reflection.

We can now define the total internal reflection as the phenomenon of reflection of light into a denser medium when the angle of incidence of a light traveling in a denser medium is greater than the critical angle of the medium.

Essential Conditions for Total Internal Reflection

There are two conditions which are essential for total internal reflection. These are:

1. The light should travel from a denser medium to a rarer medium.
2. The angle of incidence of light traveling in denser medium should be greater than the critical angle of the medium.

Total internal reflection is a very interesting phenomenon which takes place when light rays pass from an optically denser medium (e.g. water, glass) into optically rarer medium (e.g. air). Now, we shall discuss the concept of total internal reflection by taking three different cases. These are:

Case 1

Consider a point object O is placed in a tank full of water. Now, a ray of light OA starting from the point object O, bends away from the normal AN along the direction AB in the air. As the refracted ray AB is going away from the normal so the angle of refraction r is greater than the angle of incidence i.

Case 2

Now, as we increase the angle of incidence i, the angle of refraction r also increase. By increasing the angle of incidence up to a particular value which is called the critical angle (i = c), the angle of refraction r becomes equal to 900, and the refracted ray don’t go into air but gores along the horizontal water surface in the direction CD. So, critical angle may be defined as the angle of incidence in the denser medium for which the angle of refraction in rarer medium is 900. The critical angle is represented by letter ‘c’.

The value of critical angle for different substances is different, as given in table

Table of Critical Angle of different substances

Case 3

Now, if the angle of incidence i is greater than the critical angle (i.e. i > c) then the ray of light OE is reflected back into the water along the direction EF, without going into the air. This phenomenon is called total internal reflection.

We can now define the total internal reflection as the phenomenon of reflection of light into a denser medium when the angle of incidence of a light traveling in a denser medium is greater than the critical angle of the medium.

Essential Conditions for Total Internal Reflection

There are two conditions which are essential for total internal reflection. These are:

1. The light should travel from a denser medium to a rarer medium.
2. The angle of incidence of light traveling in denser medium should be greater than the critical angle of the medium.

Test Your Understanding and Answer These Questions:

1. Define critical angle.
2. What is total internal reflection? Explain with the help of a diagram.
3. Write the values of critical angle for diamond, glass and water?
4. What will be angle of refraction for a ray of light which goes from optically denser medium to optically rarer medium having angle of incidence equal to critical angle?
5. What are the essential conditions for total internal reflection to take place?

The power of a lens is defined as the ability of the lens to converge or diverge a beam of light falling on it. A lens is said to be of greater power if it diverges or converges a beam of light more strongly by focusing them closer to the optical centre. In other words, a lens of small focal length is said to have greater power. On the other hand, a lens is said to be of lesser power if it diverges or converges a beam of light to less extent. In other words, a lens of large focal length is said to be of lesser power.

Thus, the power of a lens is the reciprocal of focal length of the lens, i.e.,

       Power      =      
or
       Power      =      

       where, p = power of the lens
                  f  = focal length of the lens in meters

The power of a convex lens is positive as a convex lens has a positive focal length, while the power of a concave lens is negative as concave lens has a negative focal length.

S.I. unit of Power of Lens

The S.I. unit of power of a lens is ‘dioptre’. It is denoted by the symbol D. One dioptre is the power of a lens whose focal length is 1 meter. So, when f = 1 meter, then

       Power      =      
or
       Power      =            =      1 dioptre

Test Your Understanding and Answer These Questions:

1. What is power of a lens? Give S.I. unit of power of a lens.
2. Define 1 dioptre.
3. Find the power of a concave lens of focal length 4 m.
4. Find the focal length of a concave lens of power – 4 D.
5. A convex lens forms a real and inverted image of a needle at a distance of 50 cm from the lens. Where is the needle placed in front of the convex lens, so that this image is of the same size as the object? Also, find the power of the lens.

The magnification of a lens may be defined as the ratio of the size (height) of the image to the size (height) of the object. The magnification of a lens is represented by the letter ‘m’. Thus,

          m   =   
or
          m   =   

       Where,   h₂   =   size of image
                     h₁   =   size of object

The magnification (m) of lens can also be calculated in terms of image distance (v) and object distance (u), if we do not know the size (height) of object and image. Thus,

          m   =   

          m   =   

       Where,   v   =   image distance
                     u   =   object distance

Please note that the magnification formula is applicable both in convex lenses and concave lenses. And the magnification m is positive when the image formed is virtual and erect. On the other hand, the magnification m is negative when the image formed is real and inverted.

Test Your Understanding and Answer These Questions:

1. What do you meant by magnification of a lens?

A lens formula may be defined as the formula which gives the relationship between the distance of image (v), distance of object (u), and the focal length (f) of the lens. It may be written as:

       Where,   v   =   Distance of image from optical centre of lens
                     u   =   Distance of object from optical centre of lens
       and         f   =   Focal length of lens

       The lens formula is applicable both in convex lenses and concave lenses.

Test Your Understanding and Answer These Questions:

1. Define lens formula.
2. Is lens formula applicable only for convex lens?
3. An object 5 cm high is held 25 cm away from a converging lens of focal length 20 cm. Draw the ray diagram and find the position, size and nature of the image formed.
4. A concave lens of focal length 15 cm forms an image 10 cm from the lens. How far is the object placed from the lens? Draw the ray diagram.

For measuring the various distances in a ray diagram of refraction by spherical lenses following sign conventions are used:

1. All the distances in a ray diagram of refraction by spherical lenses are measured from the optical centre of the spherical lens.
2. The distances measured in the direction of incident light are taken as positive.
3. The distances measured in the direction opposite to the direction of incident light are taken as negative.
4. The heights measured upwards and perpendiculars to the principal axis of the lens are taken as positive.
5. The heights measured downwards and perpendiculars to the principal axis of the lens are taken as negative.

Test Your Understanding and Answer These Questions:

1. Write the New Cartesian Sign Conventions for refraction of light by spherical lenses?