Q: An object 5 cm in length is held 25 cm away from converging lens of focal length 10 cm. Draw the ray diagram and find the position, size and nature of the image formed.

Given,=5cmu=−25cmf=10cmv=?We know that,v1−u1=f1v1+251=101v1=101−251So,v1=50(5−2)That is,v1=503So,v=350=16.66cm16.66cm=uvThat is,m=−2516.66=−0.66Also,m=heightofobjectheightofimageor−0.66=5cmheightofimage=3.3cmThe negative sign of the height of image shows that an inverted image is formed.16.66cm=−3.3cmNature of image is real and inverted.

Question 1

Which one of the following materials cannot be used to make a lens?

Accepted Answer

Clay cannot be used to make a lens because if the lens is made up of clay the light rays cannot pass through it

Question 2

The image formed by a concave mirror is observed to be virtual, erect and larger than the object. Where should be the position of the object?

Accepted Answer

When the position of object is between the pole of mirror and its principal focus, the image formed by a concave mirror is observed to be virtual, erect and larger than the object.

Question 3

Where should an object be placed in front of convex lens to get a real image of the size of the object?

Accepted Answer

When object is kept at twice the focal length, image is formed at twice the focal length on the opposite side. In such a scenario, magnification is -1 and hence the image size is same as object size.

Question 4

A spherical mirror and a thin spherical lens have each a focal length of −15 cm. The mirror and lens are likely to be :

Accepted Answer

Negative focal length is a characteristic of concave mirror and concave lens. Hence, both mirror and the lens are concave.

Question 5

No matter how far you stand from a mirror, your image appears erect. The mirror is likely to be

Accepted Answer

The mirrors are likely to be either plane or convex.

Question 6

Which of the following lenses would you prefer to use while reading small letters found in a dictionary?

Accepted Answer

A convex lens forms a magnified image of the object on the other side of the lens when the object is placed between the radius of curvature and the focus of the lens.The magnification of the convex lens is larger for the smaller value of the focal length. Therefore, in order to read the small letters, the convex lens of smaller focal length will be used.Option C is correct.

Question 7

We wish to obtain an erect image of an object, using a concave mirror of focal length 15 cm. What should be the range of distance of the object from the mirror? What is the nature of the image? Is the image larger or smaller than the object? Draw a ray diagram to show the image formation in this case.

Accepted Answer

Object distance should be less than the focal length for the formation of an erect image. Hence, the range of distance of object from the mirror should be less than 15 cm i.e. from 0 to 15 cm in the front of mirror from the pole. The nature of image so formed will be virtual and erect. The size of the image will be larger than object. Ray diagram is attached as image to the question.

Question 8

Name the type of mirror used in the following situations. (a) Headlights of a car. (b) Side/rear-view mirror of a vehicle. (c) Solar furnace. Support your answer with reason

Accepted Answer

(a) Concave Mirror: Because concave mirrors can produce powerful parallel beam of light when light source is placed at their principal focus.(b) Convex Mirror: Because of its largest field of view.(c) Concave Mirror: Because it concentrates the parallel rays of sun at principal focus.

Question 9

One-half of a convex lens is covered with a black paper. Will this lens produce a complete image of the object? Verify your answers experimentally. Explain your observations.

Accepted Answer

Yes, it will produce a complete image of the object, as shown in figure. This can be verified experimentally by observing the image of a distance object like tree on a screen, when lower half of the lens is covered with a black paper. However, the intensity or brightness of image will reduce.A point on the object needs only two rays to form an image. Since the entire lens is not covered, at least two rays from each point pass through the lens, and hence, an image is formed. However, since the number of rays involved in the image formation reduces as the lens is covered, the image formed is less intense and less bright.Experiment:Apparatus needed: convex lens, candle, two black sheets of paper.Procedure:Place a lens on the table. Then light a candle and place it on one side of the lens on the table. Make the room dark by switching off the light. Take the sheet of paper and place it on the other side of the lens of the candle. Now focus the image formed on the sheet of paper by moving the sheet only. Observe the image. Mark the positions of candle, lens and screen. Now, turn off the light. Half a portion of the lens is covered with a second sheet of black paper. Mount the lens on the table in the original position and repeat the above experiment.Observations:A focused image is obtained in both experiments. However, the image formed with half the lens covered is less bright than when it is uncovered.

Question 10

An object 5 cm in length is held 25 cm away from converging lens of focal length 10 cm. Draw the ray diagram and find the position, size and nature of the image formed.

Accepted Answer

Given,=5cmu=−25cmf=10cmv=?We know that,v1​−u1​=f1​v1​+251​=101​v1​=101​−251​So,v1​=50(5−2)​That is,v1​=503​So,v=350​=16.66cm16.66cm=uv​That is,m=−2516.66​=−0.66Also,m=heightofobjectheightofimage​or−0.66=5cmheightofimage​=3.3cmThe negative sign of the height of image shows that an inverted image is formed.16.66cm=−3.3cmNature of image is real and inverted.

Question 11

A concave lens of focal length 15cm forms an image 10 cm from the lens . How far is the object placed from the lens? Draw the ray diagram.

Accepted Answer

Given: f=−15v=−10From mirror formula, v1​−u1​=f1​v1​−u1​=f1​                                    u1​=151​−101​−101​−u1​=−151​

Question 12

An object is placed at a distance of 10 cm from a convex mirror of focal length 15 cm. Find the position and nature of the image.

Accepted Answer

It is to be remembered that a convex mirror always forms the virtual, erect and diished image.Given: Object distance, u=−10cm     Focal length, f=15cmTo find: Image distance, vFrom mirror formula :v1​+u1​=f1​v1​−101​=151​v1​=151​+101​=15025​v=6cmHence image will be formed 6 cm beyond the mirror, i.e virtual magnificationm=u−v​=−10−6​=0.6Hence it will be erect and diished.

Question 13

The magnification produced by a plane mirror is +1. What does this mean?

Accepted Answer

Since magnification, m=hh​=u−ν​ . Given, m=+1 , so h′=h and v=−u (i) m=1  indicates the size of image is same as that of object.(ii) positive sign of m  indicates that an erect image is formed.The opposite signs of v and u  indicate that image is formed on the other side of the mirror from where the object is placed i.e., image is formed behind the mirror and thus image formed is virtual.

Question 14

An object 5.0cm in length is placed at a distance of 20cm in front of a convex mirror of radius of curvature 30cm. Find the position of the image, its nature, and its size.

Accepted Answer

Given: u=−20 cm            f=R/2=15 cm            Size of image, h=5 cmLet size of image be h′From mirror formula, u1​+v1​=f1​                                   −201​+v1​=151​                                   v=760​=8.57 cmThe image is formed 8.57cm behind the mirror. It is virtual and erect.Magnification, m=−v/u=8.57/20=0.428Also, m=h′/h=h′/5From above, h′/5=0.428                      h′=2.14 cm

Question 15

An object of size 7.0cm is placed at 27cm in front of a concave mirror of focal length 18cm. At what distance from the mirror should a screen be placed so that a sharp focused image can be obtained? Find the size and nature of the image.

Accepted Answer

Given:size of object, o=+7cmdistance of object ,u=−27cmfocal length of concave mirror, f=−18cmlet us take size of image=Iso, mirror formula is v1​+u1​=f1​so, putting values of u and v,v1​=−181​−−271​v1​=−541​v=−54cmso, image is formed on object side only.magnification,m=u−v​=oI​m=−−27−54​=7I​I=−14cmso, image is double in size to that of object.Nature: real, inverted and magnified image.

Question 16

Find the focal length of a lens of power (-2.0)D. What type of lens is this?

Accepted Answer

Given,  lens of power P=(−2.0)DPower, P=f1​             f=p1​                =−21​              f=−0.5 mSince focal length is negative, it is concave lens.

Question 17

A doctor has prescribed a corrective lens of power +1.5 D to a patient.  Find the focal length of the lens in centimeter.  Is the prescribed lens diverging or converging?

Accepted Answer

Given, Power, P=1.5Dfocal length in metres, f=P1​f=1.51​mf=32​m=32​×100f=66.7cmThe power is positive, lens is convex i.e., converging

Question 18

The human eye can focus objects at different distances by adjusting the focal length of the eye.This is due to:

Accepted Answer

Due to Accommodation, the human eye can focus objects at different distances.The accommodation of an eye is its reflex to adjust itself in response to focusing on a near object and then suddenly focusing on a faraway object. Option B is correct.

Question 19

The human eye forms the image of an object at its

Accepted Answer

The image of any object placed in front of the human eye is formed at the retina of the eye which is present as the screen being the eye lens.

Question 20

The least distance of distinct vision for a young adult with normal vision is about

Accepted Answer

Near point or least distinct vision - it is the distance from the eyes up to which eyes can have a clear vision is called least distinct vision. It is about 25cms for a normal healthy eye.

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