Maharashtra Board class 10 Chapter 7 lenses textbook Solutions Pdf :

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Important Points to Remember about lenses

Lenses are basically magnifying glasses with curved sides.
A lens having both spherical surfaces puffed up outwards is called a convex lens or double convex lens or biconvex lens .
A lens having both spherical surfaces curved inwards is called a concave lens or double concave lens or biconcave lens
Cornea: The cornea is a thin and transparent cover (membrane) on the human eye through which light enters the eye. Maximum refraction of light rays entering the eye occurs at the cornea.
Iris : The iris is a dark fleshy screen (muscular diaphragm) behind the cornea in the human eye. Its colours are different for different people.
Pupil : The pupil is a small circular opening of changing diameter at the centre of the iris in the human eye
Uses of a convex lens: Simple microscope, compound microscope, telescope, camera, projector, spectrometer, spectacles, etc.
Uses of a concave lens : A concave lens is used in spectacles to correct myopia. It is also used in optical instruments
Use of a telescope : A telescope is used to observe a distant object such as mountain, moon, planet, star in the magnified form
Farsightedness : In this defect the human eye can see distant objects clearly but cannot see nearby objects distinctly Nearsightedness : It’s is also called as Myopia In this case, the eye can see nearby objects clearly but the distant objects appear indistinct

Question 1. Match the following table and explain them.

Column 1	Column 2	Column 3
Farsightedness	Nearby object can be seen clearly	Bifocal lens
Presbyopia	Faraway object can be seen clearly	Concave lens
Nearsightedness	Problem of old age	Convex lens

Column 1	Column 2	Column 3
Farsightedness	Faraway object can be seen clearly	Convex lens
Presbyopia	Problem of old age	Bifocal lens
Nearsightedness	Near by object can be seen clearly	Concave lens

Answer :

Column 1 Column 2 Column 3

Farsightedness Faraway object can be
seen clearly Convex lens

Presbyopia Problem of old age Bifocal lens

Nearsightedness Near by object can be
seen clearly Concave lens

Farsightedness : 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.

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 decrease.

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.

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.

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.

Nearsightedness : It’s is also called as 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.

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. The focal length of concave lens is

negative, so a lens with negative power is required for correcting nearsightedness. .

Question 2. Draw a figure explaining various terms related to a lens.

Answer :

1. 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

sperical, has two centres of curvature C1

and C2

2. 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.

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

4. 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 rays P1 ,Q1, P2, Q2 passing through O are going along a straight line. Thus O is the optical centre of the lens.

5. Focal length : The distance between the optical centre and principal focus of a lens is called its focal length.

Question 3. At which position will you keep an

object in front of a convex lens so as

to get a real image of the same size as

the object ? Draw a figure.

Answer : At 2F1

Question 4. Give scientific resons:

a. Simple microscope is used for

watch repairs.

Answer : Simple microscope has convex lens which has the ability to produce 20 times larger as well as erect image of an object. This means the magnifying power of the microscope is very high. Thus, simple microscopes are used by watch makers to see the small parts and screws of the watch while repairing it.

b. One can sense colours only in

bright light.

Answer : The cells present on the retina and responsible for colour vision are known as cone cells. These cells become active only under bright light and remain inactive under dark. Thus, we are able sense only in bright light.

c. We can not clearly see an object

kept at a distance less than 25 cm

from the eye.

Answer : When we try to see a nearby object, the eye lens becomes more rounded and its focal length decreases. Then a clear image of the object is formed on the retina of the eye. The focal length of the eye lens cannot be decreased beyond some limit. Therefore we cannot clearly see an object kept at a distance less than 25 cm from the eye.

Question 5. Explain the working of an

astronomical telescope using

refraction of light.

Answer : : In order to view distant objects clearly in their magnified form, the telescope is used and the telescopes used to see astronomical sources such as the stars and the planets are known as astronomical telescopes.

There are two types of telescopes :

1. Refracting telescope, which uses lenses and

2. Reflecting telescope that uses mirrors as well as lenses

Working : In both the telescopes, the image formed by the objective is the object in the eyepiece, which produces the real image. Objective lenses are of large diameter and larger focal length so that the maximum amount of light coming from the distant object can be collected. However, the eyepiece is of smaller size with lesser focal length. Also, both the lenses fit inside a metallic tube in such a way that the distance between them can be changed. Meanwhile, the principal axes of both the lenses are on the same straight line. Generally, by using the same objective with different eyepieces, it is possible to get images with different magnification.

$Explain the working of an astronomical telescope using refraction of light$

Question 6. Distinguish between:

a. Farsightedness and Nearsightedness

Farsightedness	Nearsightedness
It’s is also called myopia	It’s is also called hypermetropia
In these defect human eye is unable to see nearby objects clearly	In these defect human eye is unable to see distant objects clearly
In these defect the image of a distant object is formed in front of the retina	In these defect the image of a nearby object would be formed behind the retina
This defect can be corrected by using a concave lens	This defect can be corrected by using convex lens

Answer :

Farsightedness Nearsightedness

It’s is also called myopia It’s is also called  hypermetropia

In these defect human eye is unable to
see nearby objects clearly In these defect human eye  is unable to
see distant objects clearly

In these defect the image of a distant object is
formed in front of the retina In these defect the image of a nearby object
would be formed behind the retina

This defect can be corrected by using a concave lens This defect can be corrected
by using convex lens

b. Concave lens and Convex Lens

Concave lens	Convex lens
Concave lens has its surfaces curved inwards	Convex lens has its surfaces puffed up outwards
It’s is thicker at the edges than in the middle	It’s is a thicker in the middle than at the edges
It’s can form only a virtual image	It’s can form only a real image as well as virtual images
It’s can form only a diminished image	It’s can be form a magnified diminished or the same sized image depending on the position of the object

Answer :

Concave lens Convex lens

Concave lens has its surfaces curved inwards Convex lens has its surfaces puffed up outwards

It’s is thicker at the edges than in the middle It’s is a thicker in the middle than at the edges

It’s can form only a virtual image It’s can form only a real image as well as virtual images

It’s can form only a diminished image It’s can be form a magnified diminished or the same sized image depending on the position of the object

Question 7. What is the function of iris and the muscles connected to the lens in

human eye?

Answer : Function of Iris: The iris is a muscular diaphragm that controls the size of the pupil, which in turn controls the amount of light entering the eye. It also gives colour to the eye.

Function of ciliary muscles: The eye lens is held in position by the ciliary muscles. The focal length of the eye lens is adjusted by the expansion and contraction of the ciliary muscles.

Question 8: Solve the following examples.

i. Doctor has prescribed a lens having power +1.5 D. What will be the focal length of the lens? What is the type of the lens and what must be the defect of vision?

Answer : Given

Power of lens, $P=+1.5 mathrm{D}$ Now, focal length of lens, $f=frac{1}{P}=+frac{1}{1.5}=+0.67 mathrm{~m}$

Since, the focal length is positive, the lens prescribed for correction is convex lens. Thus, the defect of vision is farsightedness or hypermetropia.

ii. 5 cm high object is placed at a distance of 25 cm from a converging lens of focal length of 10 cm. Determine the position, size and type of the image.

Answer: Given

Height of object, $h_{0}=5 mathrm{~cm}$ Object distance, $u=-25 mathrm{~cm}$ Since the lens is converging, thus it is a convex lens. Focal length of the lens, $f=10 mathrm{~cm}$ Using lens formula, $frac{1}{v}-frac{1}{u}=frac{1}{f}$

$Rightarrow frac{1}{v}=frac{1}{10}+frac{1}{-25}=frac{3}{50}$

$Rightarrow v=frac{50}{3}=16.7 mathrm{~cm}$

Thus, the image is formed $16.7 mathrm{~cm}$ right of the lens.

Now, we know $frac{v}{u}=frac{h_{mathrm{i}}}{h_{mathrm{o}}}$

$Rightarrow h_{mathrm{i}}=frac{50}{3 times-25} times 5=frac{10}{3}=-3.3 mathrm{~cm}$

The size of the image is 3.3 cm .negative sign shows that the image formed is real and inverted. Hence the image formed is real and inverted and diminished.

iii. Three lenses having power 2, 2.5 and 1.7 D are kept touching in a row. What is the total power of the lens combination?

Answer: Given

$P_{1}=2 mathrm{D}, P_{2}=2.5 mathrm{D}, P_{3}=1.7 mathrm{D}$

Let the total power of the lens combination be $P$. Thus, $P=P_{1}+P_{2}+P_{3}=2+2.5+1.7$

$=6.6 mathrm{D}$

iv. An object kept 60 cm from a lens gives a virtual image 20 cm in front of the lens. What is the focal length of the lens? Is it a converging lens or diverging lens?

Answer: Given

Object distance, $u=-60 mathrm{~cm}$ Image distance, $v=-20 mathrm{~cm}$ Using lens formula, $frac{1}{v}-frac{1}{u}=frac{1}{f}$

$Rightarrow frac{1}{f}=frac{1}{-20}-frac{1}{-60}=-frac{1}{30}$

$Rightarrow f=-30 mathrm{~cm}$

Since, the focal length is negative, the lens is a diverging lens or a concave lens.