Chapter 1 Physical Environment Light
Light is a form of energy. We are able to see objects around us with the help of light, although light itself is invisible.
If a person enters a dark room, he does not see the articles present in the room. When he or she switches on the electric lights, the objects within that room immediately become visible.
Light, emitted from some light source may come directly to our eyes or sometimes it may undergo reflection to reach our eyes after “bouncing off” from a surface(such as a mirror). Then it is called reflected light.
There is another optical phenomenon – known as refraction. In this case, when a ray of light coming from one medium, enters another medium, the direction of the ray of light changes at the surface of the separation of the two media.
We come across different instances of refraction in our daily life. When water is poured in an empty tub, the base of the tub appears to be raised. This occurs due to refraction.
Reflection of Light
1. Let us now discuss the reflection of light.
When we stand in front of a plane mirror, we see our images. The image appears to be “behind” the mirror. But we can immediately understand that light cannot pass through the mirror and go beyond it.
So, if we place a screen behind the mirror, no image will be formed on the screen. Such an image is called a virtual image. Formation of the real image with the help of magnifying glass
Let us take a magnifying glass and hold it in the sunlight above a piece of white paper, placed on the floor. We can see a round shape of light on the paper.
It is nothing but the image of the sun, which can be cast on the paper, which is the “screen” here
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2. Formation of the virtual image with the help of a mirror
When an object is placed in front of a plane mirror, its image is formed in the plane mirror. We can locate the image of the object in a plane mirror by using the laws of reflection of light.
Let us consider that a point object “A” is placed in front of a plane mirror, MM’. AB is the incident ray coming from A.
It falls perpendicularly on the mirror at B and is reflected along BA. AC and AD are two other rays of light, which are reflected along CE and DF, respectively.
If AB, EC, and FD are extrapolated behind the mirror, they meet at point A’. So, to a spectator it seems that the rays of light are coming from A’. Here A’ is the virtual image of A.
So, a virtual image is formed by the intersection of the light rays when extrapolated behind the mirror and not by their actual intersection.
The path of light rays forming a virtual image is generally shown by dotted lines or dashed lines in Real images and the path of the light rays forming them are shown by solid (i.e. continuous) lines.
Hence, there are two types of images – some of which can be cast or produced on screen while others cannot be cast on a screen. The former are called real images and the latter are called virtual images.
The image formed by the magnifying glass is real. Real images are always inverted (i.e. upside down). The image formed by a mirror is a virtual image. These images are always erect (i.e. upright).
3. Formation of the virtual image of an extended object
Considers an extended object AB placed in front of a plane mirror MM’. The light ray AC from point A is incident perpendicularly on the mirror at point C and retraces its path along CA. Another light ray AD from point A of the object is incident on the mirror at point D and gets reflected along DE.
The two reflected rays CA and DE, when extrapolated backward, intersect at point A’. Therefore, A’ is the image of point A.
Similarly, the reflection of the extended object takes place throughout the body of object AB and similar rays are plotted for the bottommost position of object B.
Hence the total image of the object AB is formed as A’B’. It is found that size of A’B’ is exactly equal to the size of AB.
The distance of object AB from the plane mirror is equal to the distance of the image from the mirror.
4. Shifting of the object and its virtual image in a plane mirror
When rays of light coming from a certain point, after reflection or refraction, meet at a point, the real image of the first point is formed.
It implies that a real image is formed by the actual intersection of light rays. This is not the case for virtual images.
Let us now take a ruler on the table and a plane mirror is placed at the zero mark of the ruler, perpendicularly with the plane of the table as
Let us now place the tip of a pencil at the “eight” mark on the ruler. This means that the tip of the pencil is 8 cm from the plane mirror.
Since the virtual image of the tip of the pencil is also formed 8 cm “behind” the mirror, so the total distance between the object (i.e. the tip of the pencil) and its virtual image is (8 + 8) cm = 16 cm. away from the plane mirror, its virtual image moves away by a distance of (20 -16) cm = 4 cm away from the object.
Similarly, it can be shown that if we move the object towards the mirror by 3 cm, the distance between the object and its virtual image is decreased by (3+3) cm = 6 cm.
So, it is seen that if we increase or decrease the distance between the mirror and the object, the distance between the object and its virtual image will be increased or decreased by a factor of two.
5. Lateral Inversion of the in-plane mirror
If we stand in front of a plane mirror and look at ourselves, we find that our images are of the same size as ours.
The image is at the same distance behind the mirror as we are in front of the mirror. The image is also erect. But if we move our right hand, the image moves its left hand.
This means that lateral inversion has taken place. Actually, in an image formed by a plane mirror, the left side of the object appears on the right side in the image whereas the appears on the right side in the image whereas the right side of the object appears on the left side of the image.
This change of sides of an object and its mirror image is called lateral inversion. In a lateral inversion, the image, therefore, undergoes a rotation of 180° the vertical axis.
So from the above observation and experimentation, we have learned some aspects of images formed by a plane mirror. They can be summarized as follows.
- Characteristics of images formed by a plane mirror
- Images are virtual and erect.
- Images appear to form as far behind the mirror as the object is in front of the mirror.
- The size of the image is exactly equal to the size of the object.
- The image of an asymmetric object is seen inverted laterally.
- No inversion of the top and bottom of an extended object occurs.
6. Formation of multiple images by plane mirrors
Let us now take two plane mirrors and place them vertically; on a white sheet of paper in such a way that the angle between them is 90°,
If we now place an object (say an eraser) between the mirrors, we can see multiple images. In fact, we can see three images when the angle between the two mirrors is 90°.
If the angle between the mirrors is 45°, then the number of images formed is 7. So, to generalize our observation,
we can say that if the angle between the two plane mirrors is x°, then the number
of images formed will be equal to (360°/x°-1), if 360°/x° is an even integer and (360°/x°),360°/x° is an odd integer
So, when two plane mirrors are placed vertically facing each other and if an object is placed between them then a large number of images are formed.
7. Images formed by two parallel plane mirrors
Two plane mirrors M1, and M2 are placed parallel to and facing each other. O is a luminous point situated between the mirrors.
From O perpendicular OT is drawn on Mx and perpendicular OV is drawn on M2 OT and OV is extended both ways. Light rays diverge from O.
We first consider a reflection of the rays from M1when is the image of O1 is such that OT = TO1
Some of these reflected rays a, b fall on M2 and appear to diverge from O2 which is the image of Or O1.O2 serves as the virtual object in front of M2 and so O1= VO2.
Again O2 acts as the virtual object ill front of and the image O3 forms, such that TO2= TO3. The same phenomenon repeats and thus a series of images form.
Similarly, starting with the rays first being reflected from the mirror M2 another series of images form.
Theoretically, an infinite number of images should form, but, as some light is absorbed during each reflection, the images become fainter and fainter.
Thus, a finite but quite large number of images are visible. Plane mirrors can be used to prepare periscopes and kaleidoscopes.
It is a simple long, tubular instrument with which a viewer can see different objects from the other side of a barrier that extends high above his or her head and are out of the direct line of sight.
It consists of a long rectangular box made of wood or metal. Two plane mirrors M1 and M2 (or in some cases two prisms) are fixed inside the box, one at the top and the other at the lower end of the box such that the mirrors face each other.
Each mirror makes a 45° angle with the axis of the periscope box. Rays of light coming from a distant object are incident on the mirror Mr. The rays get reflected by M1 and are incident on mirror M2.
The mirror M2 then reflects the reflected rays of light towards the eyes of the observer. The observer thus sees any object from the other side of a high barrier.
Soldiers use it to observe the movements of enemies keeping themselves hidden in trenches. In submarines, a periscope is used to watch the movements of the enemy vessel on the surface of the water, while remaining submerged in the water.
Sports lovers, unable to get entry into the galleries of a playground, take the help of a periscope to watch games from outside the barriers of the playground.
8. Kaleidoscope
This is a kind of funny toy that utilizes the property of formation of multiple images of an object when placed between three or more mirrors.
Suppose, three rectangular pieces of mirrors of the same size are joined together to give it a prism-like appearance.
It is joined in such a way that the reflecting surface of each mirror should face inside.
Then one of the open ends is covered by a ground glass of the required size. Some broken, colored glass pieces or colored small objects like beads, etc.
are placed within it. If this instrument is now aimed at a suitable source of light and is seen from the other open end, we can see some beautiful patterns formed due to multiple image formations by the three mirrors.
If we spin this kaleidoscope slowly, numerous colorful patterns will be created continuously.
Refraction of Light
It is our common experience that when light travels from one medium to the other, it deviates from its original path.
If we dip a pencil obliquely in a beaker containing water and observe it from a particular position as shown in it seems that the pencil is bent at the point of contact between the water surface and air.
(It is also called the air-water interface). This occurs due to the optical phenomenon known as refraction.
It means that light deviates from its path if one optical medium is changed with another optical medium or the density of the same medium changes because of variations in temperature, pressure, etc.
The path of light remains a straight line path in the second medium but it is inclined at some angle with the original path in the first medium.
The phenomenon, due to which a ray of light deviates from its original path while traveling from one optical medium to another optical medium is called refraction.
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Refraction of light in glass slab
Let us discuss the phenomenon in some detail. Let an oblique ray of light traveling through air transmits through a glass slab and then comes out of the glass slab to air again The ray AO in the first medium is called the incident ray.
If no deviation of path occurs at 0 then the light would have traveled along OA’. But the path of the light deviates at O and light moves through the glass medium along OB.
OB is the refracted ray. Again, at B there is a glass-air interface, and the deviation of the path of the light is observed and in the air medium it is refracted along BC.
BC is called the emergent ray. The angle between the incident ray and normal (i.e. NIST) is the angle of incidence (i.e. Z AON) and the angle between the refracted ray and the normal at the
2. Finding the refractive index of glass with respect to air
Let us take a white sheet of paper and place it on the surface of a table. Let us now place a glass slab and place it at the middle of the paper and draw its boundary ABCD with a pencil.
Now place two board pins P and Q in an upright position towards the AB side of the glass slab, as
Now looking from the side CD, let us fix two more board pins R and S such that these two pins and the images of pins P and Q as seen through the glass slab are in the same straight line.
The glass slab and the pins are then removed and the position of the pins is marked. Join PQ to meet AB at point O and join SR to meet CD at L.
Draw NM such that it is perpendicular to AB at point
Now with O as the center, let us draw a circle of any radius, intersecting PO at E and OL at G. Draw EF and GH in such a way that EF is perpendicular to NO and GH is perpendicular to MO.
So PQ. is the incident ray, 0 is the point of incidence, OL is the refracted ray, Z EON is the
the angle of incidence and Z LOM is the angle of refraction.
The ratio of EF and GH is determined. Now if the angle of incidence is changed, the angle of refraction will also change. But in each case the ratio, EF/GH will remain constant.
[More appropriately it can be said that if the two media are fixed and the color of the light remains unchanged during refraction, then whatever the angle of incidence, the magnitude of EF/GH remains constant.]
The ratio is called the Refractive Index of the second medium (i.e. here it is glass) with respect to the first medium (i.e. here it is air).
When refraction occurs between a vacuum and a certain medium, then the refractive index of the said medium is called Absolute Refractive Index.
The refractive index depends on the nature of the two media and on the color of a ray of light. When a ray of light travels from an optically denser medium to an optically rarer medium, then the magnitude of the refractive index for the light of different colors will be in the order: of red< green < blue < violet.
When a ray of light travels from an optically rarer medium, such as air, to an optically denser medium (say glass), the ray in the denser medium moves towards the normal and the angle of incidence is always greater than the angle of refraction (i.e. Z/ > Zr).
medium, such as glass, to an optically rarer medium (say air), then the ray of light in the rarer medium moves away from the normal and the angle of incidence is always less than the angle of refraction (i.e. Z/ < Zr).
It should be kept in mind that the density of a medium and its optical density is not the same. For example, oil is optically denser than water, but its natural density (i.e. mass per unit volume) is less than that of water.
Velocity Of Light In Rarer And Denser Medium
A medium in which light moves faster or the velocity of light is higher is optically rarer whereas a medium in which light moves slower is optically denser.
Whether a medium is optically denser or rarer depends upon its absolute refractive index. Light has a constant velocity of 3 x 108 m/s for all colors in a vacuum (or air).
However, if the light travels through any other optical medium, it is slowed down. It is this slowing down of light that is responsible for the phenomenon of refraction.
It has been found experimentally that, Absolute refractive index of a medium Velocity of light in a vacuum “ /Velocity of light in that medium
Laws of Refraction
First Law: The incident ray, the refracted ray, and the normal drawn at the point of incidence on the refracting surface lie on the same plane.
Second Law: For refraction of an obliquely incident ray of light of any given color in a given pair of optical media, the refractive index is constant, irrespective of the magnitudes of the angle of incidence and angle of refraction.
In the beginning, we had mentioned that when water is poured into an empty tub, the base of the tub appears to be raised.
This occurs due to refraction. Now we can explain this in a better way. Let us consider a point “0” at the base of the tub.
When water is poured into the tub, the light from “0” travels from water (an optically denser medium) to air (an optically rarer medium).
When the ray of light enters in air, it moves away from the normal drawn surface of separation between the two media.
If the refracted rays are extrapolated linearly backward, they meet at point “O'”, which is positioned higher than “0” So, to a viewer, it seems that the base of the tub has been raised.
4. Critical Angle
If a ray of light starting from an optically denser medium refracts in a rarer medium, for all oblique incident rays, the angle of refraction is greater than the angle of incidence.
In the adjacent AO is an obliquely incident ray. Its corresponding refracted ray is OA’ and the angle of refraction is Z NOA’ which is greater than the corresponding angle of incidence, Z AON’.
If the angle of incidence is gradually increased, the corresponding angle of refraction is also gradually increased.
This continues till for a certain angle of incidence, Z CON’ (denoted as 0C) the corresponding angle of refraction, Z GON, becomes 90°
That means the refracted ray, OG, grazes along the surface of the separation of the two media. This particular angle of incidence for which the angle of refraction becomes 90° is called the critical angle.
Its value depends on the pair of media as well as the color of the incident light.
Definition: When a ray of light of any given color tends to travel from an optically denser medium to an optically rarer medium, then for a certain angle of incidence the angle of refraction is 90°.
The corresponding angle of incidence is the critical angle of the given pair of media for the given color of light.
It is to be noted that the critical angle for a certain color of light is different in different pairs of media.
The critical angle of glass with respect to air for yellow light is 42°, but that of water with respect to air is 49°. Also, a given pair of media have different critical angles for different colors of light.
Total Internal Reflection
When a ray of light tends to travel from an optically denser medium to an optically rarer medium, then if the angle of incidence (<DON1 exceeds the critical angle (0C), the incident light totally reflects back along OR to the first medium (optically denser medium)
Refraction of light does not take place in this case. Such a phenomenon is called total internal reflection.
The term “total” is used because of the incident media. The points at which total internal light totally reflects back into the same denser reflection takes place look very bright,
as the medium from the surface of separation of the two incident lights reflects totally from these points.
The conditions required for the total internal reflection to take place are :
- light rays should travel from the denser to the rarer medium.
- The angle of incidence should be greater than the critical angle for the pair of media involved
- Phenomena related to total internal reflection
1. Brightness of diamonds or gems
Usually, diamonds and other gems are constituted of materials of high refractive index, the critical angle of each of which with respect to air is thus very small.
For example, the critical angle of a diamond is only 24.5°. Also, diamonds or any other gem is cut in such a way that, light can get into it through all surfaces but can emerge from very few surfaces.
This is because, the diamond or the gemstone is cut in such a way, that the rays within the “body” trying to come out are incident on most of the surfaces at an angle exceeding the critical angle.
After undergoing several total internal reflections the light rays are incident on a small number of surfaces at angles less than the critical angle and emerge from those surfaces only.
Hence, the emergent light is very intense, and that is why a diamond or a gem looks very bright.
2. A crack in the glass of a window pane looks shiny
Some air is present in the gap of a crack in the glass. So, light rays pass through the denser medium (i.e. glass)
when tend to pass through the rarer medium (i.e. air), and total internal reflection occurs at some point in the crack. Hence those points of the crack look shiny.
3. An empty test tube dipped in the water looks shiny
An empty test tube is dipped in water in an inclined way. Light rays passing through water outside the tube tend to pass through air present in the empty test tube.
Thus light passes from an optically denser medium to an optically rarer medium. At some points on the surface of the test tube, rays of light are incident at angles exceeding the critical angle of water to air.
At those points total internal reflection takes place and so the empty portion of the test tube looks bright when viewed from above vertically
4. Drop Of Water On the Arum Leaf Seems Glittering
This is because when a ray of light travels from inside the water droplet to the air, the angle of incidence exceeds the critical angle of the two media (i.e. water and air).
So, total internal reflection occurs at the surface of the separation between water and air. When the emerging ray of light reaches to viewer’s eye, the viewer finds the area glittering.
5. Mirage in the desert
In deserts, during day time, the sand bed becomes extremely hot. So the air just above it is also heated and the density of air decreases.
With increasing altitude, the successive layers of the air have gradually increasing density. In absence of any flow of air, this is maintained for a long time.
Let us consider a light ray coming from point “A” on top of a tree in the desert moving downwards
As the density of air decreases downwards, and as the ray of light moves downwards through different layers (of decreasing density), the angle of refraction increases progressively.
At some interface between two layers of air, the angle of incidence is greater than the critical angle, and it suffers total internal reflection and consequently moves upwards.
As it moves upwards from a rarer medium to a denser medium, the ray of light bends towards the normal. When the ray reaches an observer, he or she “secs” a virtual image of A at A7.
In this way, rays coming from different parts of the object (i.e. tree) reach to viewer’s eye after suffering total internal reflection.
Ultimately the viewer sees an inverted, virtual image of the original object in a direction far away from the original position of the object.
Due to variations in temperature, the density of different layers of air changes continuously, and to an observer, the image seems shimmering.
The observer thinks this inverted, shimmering image of the tree is the reflection of the tree formed on the water surface below the tree and the viewer is totally misguided. This optical illusion is called a mirage.
6. Mirage in the cold country
In colder countries, the air in contact with water is denser and with increasing altitude, the density of air decreases.
For our convenience, we can think of different layers of air of decreasing density with increasing altitude.
The rays of light from a boat far away from the jetty, when going in an upward direction, it travels from a denser to a rarer medium.
In each layer, the refracted ray moves away progressively from the normal and the angle of incidence increases gradually.
Ultimately, a point is reached when the angle of incidence becomes greater than the critical angle of the two adjacent layers of air and the incident ray suffers total internal reflection at that particular interface
(or surface of separation) and bends downwards. When it reaches the viewer’s eye, the viewer sees a virtual image of the boat which is inverted, moving in the sky.
