Lenses Class 10 Science Notes Maharashtra Board

Lenses Class 10 Science Notes Maharashtra State Board

Lenses
You must have seen lenses used in day-to-day life. Some examples are the lenses used by old persons for reading, the lens embedded in the front door of the house, the lens that the watchmaker attaches to his eye, etc. Lenses are used in spectacles. They are also used in telescopes as you have learned 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 center as compared to the edges. The lens with both surfaces spherical inside is called a concave or double concave lens. This lens is thinner at the center as compared to its edges.

Different types of lenses are shown in the figure. 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 the figure. The surface marked as 1 is part of sphere S₁ while surface 2 is part of sphere S₂.

Centre of Curvature (C):
The centers of spheres whose parts form surfaces of the lenses are called centers of curvatures of the lenses. A lens with both surfaces is spherical and has two centers 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 the figure, rays P₁Q₁, and P₂Q₂ 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 F₁ 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 traveling 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 F₁ 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 the principal focus of a lens is called its focal length.

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 lense 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 What is the distance 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 learned 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 the 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.

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

Method:

• Draw a straight line along the centre of a long table.
• Place the lens on the stand at the central point (O) of the line.
• Place the screen on one side, of the lens. Move it along the line to get a clear image of a distant object. Mark its position as F₁.
• 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.
• Repeat actions 3 and 4 on the other side of the lens and mark F₂ and 2F₂ on the straight line.
• Now place the burning candle on the other side of the 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.
• 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, 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 A’B’ 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 are formed by convex lenses for different positions of the object.

Position of the Object	Position of the Image	Size of the Image	Nature of the Image
1. At infinity	At focus F2	Point Image	Real and Inverted
2. Beyond 2F1	Between F2 and 2F2	Smaller	Real and Inverted
3. At 2F1	At 2F2	Same Size	Real and Inverted
4. Between F1 and 2F1	Beyond 2F2	Larger	Real and Inverted
5. At focus F1	At infinity	Very Large	Real and Inverted
6. Between F1 and O	On the same side of the lens as the object	Very Large	Virtual and Erect

Images formed by Concave Lenses
We can obtain the images obtained by concave lenses using the following rules.

• When the incident ray is parallel to the principal axis, the refracted ray when extended backward, passes through the focus.
• When the incident ray passes through the focus, the refracted ray is parallel to the principal axis.

As shown in the figure, 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 backward, 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 point Q is on the principal axis, its image is formed along the axis at the point Q₁ directly below P₁. Thus, P₁Q₁ is the image of PQ. The image formed by a concave lens is always virtual, erect, and smaller than the object.

Position of the Object	Position of the Image	Size of the Image	Nature of the Image
1. At infinity	On the first focus F1	Point Image	Virtual and Erect
2. Anywhere between optical centre O and infinity	Between the optical centre and focus F1	Small	Virtual and Erect

Sign Convention

Lens Formula
The formula showing the relation between the 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.
\(\frac{1}{v}-\frac{1}{u}=\frac{1}{f}\)
The lens formula is the same for any spherical lens and any distance of the object from the lens. It is however necessary to use the sign convention properly.

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.

• 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).
• The distance d measured to the right of O is taken to be positive while those measured to the left are taken to be negative.
• Distances perpendicular to the principal axis and above it are taken to be positive.
• Distances perpendicular to the principal axis and below it are taken to be negative.
• 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 object’s height (h₁).
Magnification = \(\frac{Height of the Image}{Height of the Object}\)
i.e. M = \(\frac{\mathrm{h}_2}{\mathrm{~h}_1}\) ……………… (1)
The magnification due to a lens is also related to the distance of the object (u) and that of the image (v) from the lens.
Magnification = \(\frac{Distance of the Image}{Distance of the Object}\)
i.e. M = \(\frac{v}{u}\) ……………… (2)

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).
P = \(\frac{1}{\mathrm{f}(\mathrm{m})}\)
1 Dioptre = \(\frac{1}{1 m}\)

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 \(\frac{1}{f}=\frac{1}{f_1}+\frac{1}{f_2}\).
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 powers.

Solved Examples

Example 1.
An object is placed vertically at a distance of 20 cm from a convex lens. If the height of the object is 5 cm and the focal length of the lens is 10 cm, what will be the position, size, and nature of the image? How much bigger will the image be as compared to the object?
Given:
Height of the object (h₁) = 5 cm,
focal length (f) = 10 cm,
distance of the object (u) = -20 cm
Image distance (v) = ?
Height of the image (h₂) = ?
Magnification (M) = ?

The positive sign of the image distance shows that the image is formed at 20 cm on the other side of the lens.

The negative sign of the height of the image and the magnification shows that the image is inverted and real. It is below the principal axis and is of the same size as the object.

Example 2.
The focal length of a convex lens is 20 cm. What is its power?
Given:
Focal length = f = 20 cm = 0.2 m
Power of the lens = P = ?
P = \(\frac{1}{\mathrm{f}(\mathrm{m})}\)
= \(\frac{1}{0.2}\)
= 5D
The power of the lens is 5D.

Human Eye and Working of its Lens
There is a very thin transparent cover (membrane) on the human eye. This is called cornea. Light enters the eye through it. The 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, the pupil contracts while if the light is dim, it widens.

On the surface of the iris, there is a 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 a 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 the optic nerve. Later, the brain analyses these signals and converts them in such a way that we perceive the objects as they 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. While seeing nearby objects the lens becomes more rounded and its focal length decreases as shown in part b of the figure. This way we can see objects 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 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 visible without stress on the eye is called the 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.

The eyeball is approximately spherical and has a diameter of about 2.4 cm. The working of the lens in the 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.

Defects of Vision and their Corrections
Some people can not see things clearly due to the 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. There are two reasons for this defect.

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

This defect can be corrected by using spectacles with concave lenses 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 the 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, the images of nearby objects get formed behind the retina. There are two reasons for farsightedness.

• Curvature of the cornea and the eye lens decreases so that, the converging power of the lens becomes less.
• Due to the flattening of the eyeball, 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 have 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. 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 the concave lens and corrects nearsightedness while the lower part is a convex lens which corrects the farsightedness.

Apparent Size of an Object
Consider two objects, PQ and P₁Q₁, having the same size but kept at different distances from an eye as shown in the figure. As the angle α subtended by PQ at the eye is larger than the angle β subtended by P₁Q₁, PQ appears bigger than P₁Q₁. Thus, the apparent size of an object depends on the angle subtended by the object at the eye.

Use of Concave Lenses

• Medical equipment, scanner, CD player – These instruments use laser light. For proper working of this equipment, concave lenses are used.
• The peephole in the door – This is a small safety device that helps us see a large area outside the door. This uses one or more concave lenses.
• Spectacles – Concave lenses are used in spectacles to correct nearsightedness.
• Torch – A concave lens is used to spread widely the light produced by a small bulb inside a torch.
• 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

Simple Microscope:
A convex lens with a small focal length produces a virtual, erect, and bigger image of an object as shown in the figure. Such a lens is called a 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.

Compound Microscope:
A 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 a simple microscope. Compound microscopes are used to study these objects. A compound microscope is made of two convex lenses: objective and eyepiece. The objective has a smaller cross-section and smaller focal length. The eyepiece has a bigger cross-section, and 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, 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 them can be changed.

Telescope:
The 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.

• Refracting telescope – This uses lenses.
• Reflecting telescope – This uses mirrors and lenses.

In both of these, the image formed by the objective acts as an object for the eyepiece which forms the final image. An objective lens has a large diameter and larger focal length because of which the maximum amount of light coming from a distant object can be collected.

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

Optical Instrument:
Convex lenses are used in various other optical instruments like cameras, projectors, spectrographs, etc.

Spectacles:
Convex lenses are used in spectacles for correcting farsightness.

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 the retina persists for a while. This is called the 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. The 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 eyesight is normal.

Comprehensive Maharashtra State Board Class 10 Science Notes Lenses can help students make connections between concepts.