Lenses

You must have seen lenses used in day to day life. Some examples are: the lenses used by old persons for reading, lens embedded in the front door of the house, the lens which the watch maker attaches to his eye etc. Lenses are used in spectacles. They are also used in telescopes as you have learnt in the previous standard.

A lens is a transparent medium bound by two surfaces. The lens which has two spherical surfaces which are puffed up outwards is called a convex or double convex lens. This lens is thicker near the centre as compared to the edges.

The lens with both surfaces spherical on the inside is called a concave or double concave lens. This lens is thinner at the centre as compared to its edges. Different types of lenses are shown in figure 7.2. A ray of light gets refracted twice while passing through a lens, once while entering the lens and once while emerging from the lens. The direction of the ray changes because of these refractions. Both the surfaces of most lenses are parts of a sphere.

The cross-sections of convex and concave lenses are shown in parts a and b of figure 7.3. The surface marked as 1 is part of sphere S1 while surface 2 is part of sphere S2 .

Centre of curvature (C) : The centres of spheres whose parts form surfaces of the lenses are called centres of curvatures of the lenses. A lens with both surfaces spherical, has two centres of curvature C1 and C2 .

Radius of curvature (R) : The radii (R1 and R2 ) of the spheres whose parts form surfaces of the lenses are called the radii of curvature of the lens.

Principal axis : The imaginary line passing through both centres of curvature is called the principal axis of the lens.

Optical centre (O) : The point inside a lens on the principal axis, through which light rays pass without changing their path is called the optical centre of a lens. In figure 7.4, rays P1 Q1 , P2 Q2 passing through O are going along a straight line. Thus O is the optical centre of the lens.

Principal focus (F) : When light rays parallel to the principal axis are incident on a convex lens, they converge to a point on the principal axis. This point is called the principal focus of the lens. As shown in figure 7.5a F1 and F2 are the principal foci of the convex lens. Light rays parallel to the principal axis falling on a convex lens come together i.e. get focused at a point on the principal axis. So this type of lens is called a converging lens. Rays travelling parallel to the principal axis of a concave lens diverge after refraction in such a way that they appear to be coming out of a point on the principal axis. This point is called the principal focus of the concave lens. As shown in figure 7.5b F1 and F2 are the principal foci of the concave lens.

Light rays parallel to the principal axis falling on a concave lens go away from one another (diverge) after refraction. So this type of lens is called a divergent lens. Focal length (f) : The distance between the optical centre and principal focus of a lens is called its focal length.

Try this.

Material: Convex lens, screen, meter scale, stand for the lens etc.

Method: Keeping the screen fixed, obtain a clear image of a distant object like a tree or a building with the help of the lens on the screen. Measure the distance between the screen and the lens with the help of the meter scale. Now turn the other side of the lens towards the screen. Again obtain a clear image of the distant object on the screen by moving the lens forward or backward. Measure the distance between the screen and the lens again.

What is this distance between the lens and the screen called? Discuss the relation between this distance and the radius of curvature of the lens with your teacher. The image of a distant object is obtained close to the focus of the lens, hence, the above distance is the focal length of the lens. What will happen if you use a concave lens in this experiment?

Ray diagram for refraction :

You have learnt the rules for drawing ray diagrams for spherical mirrors. Similarly, one can obtain the images formed by lenses with the help of ray diagrams. One can obtain the position, size and nature of the images with the help of these diagrams.

Images formed by convex lenses

 One can use following three rules to draw ray diagrams of images obtained by convex lenses.

Rule 1: When the incident ray is parallel to the principal axis, the refracted ray passes through the principal focus.

Rule 2: When the incident ray passes through the principal focus, the refracted ray is parallel to the principal axis.

Rule 3: When the incident ray passes through the optical centre of the lens, it passes without changing its direction.

Try This

Material: A convex lens, screen, meter scale, stand for the lens, chalk, candle etc.

Method: 1. Draw a straight line along the centre of a long table.

2. Place the lens on the stand at the central point (O) of the line.
3. Place the screen on one side, of the lens. Move it along the line so as to get a clear image of a distant object. Mark its position as F1 .
4. Measure the distance between O and F1 . Mark a point at distance 2F1 from O on the same side of F1 and mark it as 2F1 .
5. Repeat actions 3 and 4 on the other side of the lens and mark F2 and 2F2 on the straight line.
6. Now place the burning candle on the other side of lens far beyond 2F1 . Place the screen on the opposite side of the lens and obtain a clear image of the candle by moving it forward or backward along the line. Note the position, size and nature of the image.
7. Repeat action 6 by placing the candle beyond 2F1 , at 2F1 , between 2F1 and F1 , at F1 and between F1 and O. Note your observations.

As shown in the figure 7.7, an object AB is placed beyond the point 2F1 . The incident ray BC, starting from B and going parallel to the principal axis, goes through the principal focus F2 after refraction along CT. The ray BO, starting from B and passing through the optical centre O of the lens goes along OS without changing its direction. It intersects CT in B¢ . This means that the image of B is formed at B¢ .

As A is situated on the principal axis, its image will also be located along the principal axis at A¢ , vertically above B¢ . Thus, A¢ B¢ will be the image of AB formed by the lens. So we learn that if an object is placed beyond 2F1 , the image is formed between F2 and 2F2 . It is real and inverted and its size is smaller than that of the object.

Images formed by concave lenses

We can obtain the images obtained by concave lenses using the following rules.

1. When the incident ray is parallel to the principal axis, the refracted ray when extended backwards, passes through the focus.
2. When the incident ray passes through the focus, the refracted ray is parallel to the principal axis.

As shown in figure 7.9, object PQ is placed between F1 and 2F1 in front of a concave lens. The incident ray PA, starting from P and going parallel to the principal axis goes along AD after refraction. If AD is extended backwards, it appears to come from F1 . The incident ray PO, starting from P and passing through O, goes along the same direction after refraction. PO intersects the extended ray AF1 at P1 , i.e. P1 is the image of P.

As the point Q is on the principal axis, its image is formed along the axis at the point Q1 directly below P1 . Thus, P1 Q1 is the image of PQ. The image formed by a concave lens is always virtual, erect and smaller than the object.

Lens formula

The formula showing the relation between distance of the object (u), the distance of the image (v) and the focal length (f) is called the lens formula. It is given below.

According to the Cartesian sign convention, the optical centre (O) is taken to be the origin. The principle axis is the X-axis of the frame of reference. The sign convention is as follows. 1. The object is always placed on the left of the lens, All distances parallel to the principal axis are measured from the optical centre (O). 2. The distanced measured to the right of O are taken to be positive while those measured to the left are taken to be negative. 3. Distances perpendicular to the principal axis and above it are taken to be positive. 4. Distances perpendicular to the principal axis and below it are taken to be negative. 5. The focal length of a convex lens is positive while that of a concave lens is negative.

Magnification (M)

The magnification due to a lens is the ratio of the height of the image (h2 ) to the height of the object (h1 ).

Take two convex lenses of different sizes. Collect sunlight on a paper using one of the lenses. The paper will start burning after a while. Note the time required for the paper to start burning. Repeat the process for the second lens. Is the time required the same in both cases? What can you tell from this ?

Power of a lens

 The capacity of a lens to converge or diverge incident rays is called its power (P). The power of a lens depends on its focal length. Power is the inverse of its focal length (f); f is expressed in meters. The unit of the power of a lens is Dioptre (D).

Combination of lenses

If two lenses with focal lengths f1 and f2 are kept in contact with each other, the combination has an effective focal length given by

If the powers of the two lenses are P1 and P2 then the effective power of their combination is P = P1 + P2 . Thus, when two lenses are kept touching each other, the power of the combined lens is equal to the sum of their individual powers.

Human eye and working of its lens

There is a very thin transparent cover ( membrane) on the human eye. This is called cornea (fig 7.11). Light enters the eye through it. Maximum amount of incident light is refracted inside the eye at the outer surface of the cornea. There is a dark, fleshy screen behind the cornea. This is called the Iris. The colour of the Iris is different for different people. There is a small hole of changing diameter at the centre of the Iris which is called the pupil. The pupil controls the amount of light entering the eye. If the light falling on the eye is too bright, pupil contracts while if the light is dim, it widens. On the surface of the iris, there is bulge of transparent layers. There is a double convex transparent crystalline lens, just behind the pupil. The lens provides small adjustments of the focal length to focus the image. This lens creates real and inverted image of an object on the screen inside the eye. This screen is made of light sensitive cells and is called the retina. These cells get excited when light falls on them and generate electric signals. These signals are conveyed to the brain through optic nerve. Later, the brain analyses these signals and converts them in such a way that we perceive the objects as they actually are.

While seeing objects at large, infinite distances, the lens of the eye becomes flat and its focal length increases as shown in part a of the figure 7.12. While seeing nearby objects the lens becomes more rounded and its focal length decreases as shown in part b of the figure 7.12. This way we can see objects clearly irrespective of their distance.

The capacity of the lens to change its focal length as per need is called its power of accommodation. Although the elastic lens can change its focal length, to increase or decrease it, it can not do so beyond a limit.

The minimum distance of an object from a normal eye, at which it is clearly visible without stress on the eye, is called as minimum distance of distinct vision. The position of the object at this distance is called the near point of the eye, for a normal human eye, the near point is at 25 cm. The farthest distance of an object from a human eye, at which it is clearly visible without stress on the eye is called farthest distance of distinct vision. The position of the object at this distance is called the far point of the eye. For a normal human eye, the far point is at infinity

Do you know ?

The eye ball is approximately spherical and has a diameter of about 2.4 cm. The working of the lens in human eye is extremely important. The lens can change its focal length to adjust and see objects at different distances. In a relaxed state, the focal length of healthy eyes is 2 cm. The other focus of the eye is on the retina.

Try this.

Defects of Vision and their corrections

Some people can not see things clearly due to loss of accommodation power of the lenses in their eyes. Because of defective refraction by the lenses their vision becomes faint and fuzzy. In general, there are three types of refraction defects.

1. Nearsightedness/ Myopia

In this case, the eye can see nearby objects clearly but the distant objects appear indistinct. This means that the far point of the eye is not at infinity but shifts closer to the eye. In nearsightedness, the image of a distant object forms in front of the retina (see figure 7.13). There are two reasons for this defect.

1. The curvature of the cornea and the eye lens increases.The muscles near the lens can not relax so that the converging power of the lens remains large.
2. The eyeball elongates so that the distance between the lens and the retina increases.

This defect can be corrected by using spectacles with concave lens of proper focal length. This lens diverges the incident rays and these diverged rays can be converged by the lens in the eye to form the image on the retina. The focal length of concave lens is negative, so a lens with negative power is required for correcting nearsightedness. The power of the lens is different for different eyes depending on the magnitude of their nearsightedness.

2. Farsightedness or hypermetropia

In this defect the human eye can see distant objects clearly but cannot see nearby objects distinctly. This means that the near point of the eye is no longer at 25 cm but shifts farther away. As shown in the figure (7.14), the images of nearby objects get formed behind the retina. There are two reasons for farsightedness.

1. Curvature of the cornea and the eye lens decreases so that, the converging power of the lens becomes less.
2. Due to the flattening of the eye ball the distance between the lens and retina decreases.

This defect can be corrected by using a convex lens with proper focal length. This lens converges the incident rays before they reach the lens. The lens then converges them to form the image on the retina. The focal length of a convex lens is positive thus the spectacles used to correct farsightedness has positive power. The power of these lenses is different depending on the extent of farsightedness

3. Presbyopia

Generally, the focusing power of the eye lens decreases with age. The muscles near the lens lose their ability to change the focal length of the lens. The near point of the lens shifts farther from the eye. Because of this old people cannot see nearby objects clearly.

Sometimes people suffer from nearsightedness as well as farsightedness. In such a case bifocal lenses are required to correct the defect. In such lenses, the upper part is concave lens and corrects nearsightedness while the lower part is a convex lens which corrects the farsightedness.

Try this.

1. Make a list of students in your class using spectacles.
2. Record the power of their lenses. Find out and note which type of defect of vision they suffer from. Which defect is most common among the students?

Apparent size of an object

Consider two objects, PQ and P1 Q1 , having same size but kept at different distances from an eye as shown in figure 7.15. As the angle α subtended by PQ at the eye is larger than the angle β subtended by P1 Q1 , PQ appears bigger than P1 Q1 . Thus, the apparent size of an object depends on the angle subtended by the object at the eye.

Use of concave lenses

1. Medical equipments, scanner, CD player – These instuments use laser light. For proper working of these equipments concave lenses are used.
2. The peep hole in door- This is a small safety device which helps us see a large area outside the door. This uses one or more concave lenses.
3. Spectacles- Concave lenses are used in spectacles to correct nearsightedness.
4. Torch- Concave lens is used to spread widely the light produced by a small bulb inside a torch.
5. Camera, telescope and microscope- These instruments mainly use convex lenses. To get good quality images a concave lens is used in front of the eyepiece or inside it.

Use of convex lenses

1. Simple microscope : A convex lens with small focal length produces a virtual, erect and bigger image of an object as shown in the figure. Such a lens is called simple microscope or magnifying lens. One can get a 20 times larger image of an object using such microscopes. These are used for watch repair, testing precious gems and finding their defects.
2. Compound microscope Simple microscope is used to observe small sized objects. But minute objects like blood cells, cells of plants and animals and minute living beings like bacteria cannot be magnified sufficiently by simple microscope. Compound microscopes are used to study these objects. A compound microscope is made of two convex lenses: objective and eye piece. The objective has smaller cross-section and smaller focal length. The eye piece has bigger cross[1]section, its focal length is also larger than that of the objective. Higher magnification can be obtained by the combined effect of the two lenses.

As shown in the figure 7.17, the magnification occurs in two stages. The image formed by the first lens acts as the object for the second lens. The axes of both lenses are along the same line. The lenses are fitted inside a metallic tube in such a way that the distance between can be changed.

1. Telescope

 Telescope is used to see distant objects clearly in their magnified form. The telescopes used to observe astronomical sources like the stars and the planets are called astronomical telescopes. Telescopes are of two types. 1. Refracting telescope – This uses lenses 2. Reflecting telescope – This uses mirrors and also lenses. In both of these, the image formed by the objective acts as object for the eye piece which forms the final image. Objective lens has large diameter and larger focal length because of which maximum amount of light coming from the distant object can be collected.

On the other hand the size of the eyepiece is smaller and its focal length is also less. Both the lenses are fitted inside a metallic tube in such a way that the distance between them can be changed. The principal axes of both the lenses are along the same straight line. Generally, using the same objective but different eye pieces, different magnification can be obtained.

1. Optical instrument

Convex lenses are used in various other optical instruments like camera, projector, spectrograph etc.

Persistence of vision

We see an object because the eye lens creates its image on the retina. The image is on the retina as long as the object is in front of us. The image disappears as soon as the object is taken away. However, this is not instantaneous and the image remains imprinted on our retina for 1/16th of a second after the object is removed. The sensation on retina persists for a while. This is called persistence of vision. What examples in day to day life can you think about this?

The retina in our eyes is made up of many light sensitive cells. These cells are shaped like a rod and like a cone. The rod like cells respond to the intensity of light and give information about the brightness or dimness of the object to the brain. The conical cells respond to the colour and give information about the colour of the object to the brain. Brain processes all the information received and we see the actual image of the object. Rod like cells respond to faint light also but conical cells do not. Thus we perceive colours only in bright light. The conical cells can respond differently to red, green and blue colours. When red colour falls on the eyes, the cells responding to red light get excited more than those responding to other colours and we get the sensation of red colour. Some people lack conical cells responding to certain colours. These persons cannot recognize those colours or cannot distinguish between different colours. These persons are said to be colour blind. Apart from not being able to distinguish between different colours, their eye sight is normal.