Q: Find the size, nature and position of image formed when an object of size \$1cm\$ is placed at a distance of \$15\ cm\$ from a concave mirror of focal length \$10cm\$?

\$u=-15\$cm\$f=-10\$cm\$h=1\$cmFrom mirror formula\$\dfrac{1}{f}=\dfrac{1}{u}+\dfrac{1}{v}\$\$\dfrac{1}{v}=\dfrac{1}{f}-\dfrac{1}{u}\$\$\dfrac{1}{v}=\dfrac{1}{-10}-\dfrac{1}{-15}\$\$v=-30\$cmThe image is formed at a distance \$30\$cm on the left side of the mirror from the pole.\$m=\dfrac{h'}{h}=\dfrac{-v}{u}\$\$h'=-1\times \dfrac{-30}{-15}\$\$h=-2\$cmThe image size is \$2\$cm and it is real and inverted.

Q: 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.

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.

Q: An object is placed at (i) \$10\ cm\$, (ii) \$5\ cm\$ in front of a concave mirror of radius of curvature \$15\ cm\$. Find the position, nature and magnification of the image in each case.

(a) In concave mirror, using sign convention \$ u=-10\,cm \$ \$ R=-15\,cm \$ \$ f=\dfrac{-15}{2}\,cm \$ Using mirror’s relation \$ \dfrac{1}{v}+\dfrac{1}{u}=\dfrac{1}{f} \$ \$ \dfrac{1}{v}=\dfrac{1}{f}-\dfrac{1}{u} \$ \$ \dfrac{1}{v}=-\dfrac{2}{15}+\dfrac{1}{10} \$ \$ \dfrac{1}{v}=\dfrac{-1}{30} \$ \$ v=-30\,cm \$ Image is real and it forms at a distance of 30 cm in front of mirror. Magnification \$ m=\dfrac{-v}{u} \$ \$ m=\dfrac{30}{-10}=-3 \$ This shows image is inverted and 3 times magnified. (b) again using sign convention \$ u=-5\,cm \$ \$ f=\dfrac{-15}{2}\,cm \$ \$ \dfrac{1}{v}=\dfrac{1}{f}-\dfrac{1}{u} \$ \$ \dfrac{1}{v}=\dfrac{1}{15} \$ \$ v=+15\,cm \$ Image is formed at a distance of 15 cm behind the mirror. Magnification \$ m=\dfrac{-v}{u} \$ \$ =\dfrac{-15}{-5} \$ \$ =3 \$ +3 magnification shows image is virtual and erect.

Q: Explain why a ray of light passing through the centre of curvature of a concave mirror gets reflected along the same path after reflection.

This is because the angle of incidence is \$ 0^{\circ} \$ . That is the ray passing through the centre of curvature is incident normally to the mirror. The angle of reflection should also be \$ 0^{\circ} \$ .

Question 1

Find the size, nature and position of image formed when an object of size $1cm$ is placed at a distance of $15\ cm$ from a concave mirror of focal length $10cm$?

Accepted Answer

$u=-15$cm$f=-10$cm$h=1$cmFrom mirror formula$\dfrac{1}{f}=\dfrac{1}{u}+\dfrac{1}{v}$$\dfrac{1}{v}=\dfrac{1}{f}-\dfrac{1}{u}$$\dfrac{1}{v}=\dfrac{1}{-10}-\dfrac{1}{-15}$$v=-30$cmThe image is formed at a distance $30$cm on the left side of the mirror from the pole.$m=\dfrac{h'}{h}=\dfrac{-v}{u}$$h'=-1\times \dfrac{-30}{-15}$$h=-2$cmThe image size is $2$cm and it is real and inverted.

Question 2

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&#10;less than the focal length for the formation of an erect image. Hence, the&#10;range of distance of object from the mirror should be less than 15 cm i.e. from&#10;0 to 15 cm in the front of mirror from the pole. The nature of image so formed&#10;will be virtual and erect. The size of the image will be larger than&#10;object. Ray diagram is attached as image to the question.

Question 3

An object is placed at (i) $10\ cm$, (ii) $5\ cm$ in front of a concave mirror of radius of curvature $15\ cm$. Find the position, nature and magnification of the image in each case.

Accepted Answer

(a) In concave mirror, using sign convention&#10;&#10;$ u=-10\,cm $&#10;&#10;$ R=-15\,cm $&#10;&#10;$ f=\dfrac{-15}{2}\,cm $&#10;&#10;Using mirror&#8217;s relation&#10;&#10;$ \dfrac{1}{v}+\dfrac{1}{u}=\dfrac{1}{f} $&#10;&#10;$ \dfrac{1}{v}=\dfrac{1}{f}-\dfrac{1}{u} $&#10;&#10;$ \dfrac{1}{v}=-\dfrac{2}{15}+\dfrac{1}{10} $&#10;&#10;$ \dfrac{1}{v}=\dfrac{-1}{30} $&#10;&#10;$ v=-30\,cm $&#10;&#10;Image is real and it forms at a distance of 30 cm in front&#10;of mirror.&#10;&#10;Magnification&#10;&#10;$ m=\dfrac{-v}{u} $&#10;&#10;$ m=\dfrac{30}{-10}=-3 $&#10;&#10;This shows image is inverted and 3 times magnified.&#10;&#10;(b) again using sign convention&#10;&#10;$ u=-5\,cm $&#10;&#10;$ f=\dfrac{-15}{2}\,cm $&#10;&#10;$ \dfrac{1}{v}=\dfrac{1}{f}-\dfrac{1}{u} $&#10;&#10;$ \dfrac{1}{v}=\dfrac{1}{15} $&#10;&#10;$ v=+15\,cm $&#10;&#10;Image is formed at a distance of 15 cm behind the mirror.&#10;&#10;Magnification&#10;&#10;$ m=\dfrac{-v}{u} $&#10;&#10;$ =\dfrac{-15}{-5} $&#10;&#10;$ =3 $&#10;&#10;+3 magnification shows&#10;image is virtual and erect.

Question 4

(a) Draw ray - diagrams to show the formation of images when the object is placed in front of a concave mirror (converging mirror):
(i) between its pole and focus
(ii) between its centre of curvature and focus. Describe the nature, size and position of the image formed in each case.
(b) State one use of concave mirror based on the formation of images as in case (z) above.

Accepted Answer

(i) When an object is placed between the pole and focus of a concave mirror, the image is formed behind the mirror, it is virtual, erect and larger than the object.(ii) When the object is placed between center of curvature and principal focus of a concave mirror the image formed is beyond C  and it is real, inverted and magnified.b. For the first case it is used as shaving mirror.      For the second case it is are useful tools for determining the location of an        image as produced by a concave mirror.

Question 5

Draw a ray diagram to show the formation of image by a concave mirror for an object beyond its center of curvature. State three characteristics of the image.

Accepted Answer

The following diagram shows the formation of image by a concave mirror for an object beyond its center of curvature.The image is formed between the center of curvature C and the focus F, when an object is placed beyond the center of curvature C. The three characteristics of the image are as follows :The images are realThe images are diminished The images are inverted

Question 6

Which of the following can make a parallel beam of light when light from a point source is incident on it?

Accepted Answer

When light rays from a point source is incident on concave mirror and convex lens, emergent beams are parallel and the image is formed at infinity.Convex mirror and concave lens on the other hand always form a virtual image. Emergent beams from these are not parallel but diverging when the object is kept at focus.

Question 7

Explain why a ray of light passing through the centre of curvature of a concave mirror gets reflected along the same path after reflection.

Accepted Answer

This is because the angle of incidence is $ 0^{\circ} $ . That is the ray passing through the centre of curvature is incident normally to the mirror. The angle of reflection should also be $ 0^{\circ} $  .

Question 8

In torches, search lights and headlights of vehicles the bulb is placed:

Accepted Answer

In torches, search lights and headlights of vehicles the bulb is placed very near to the focus of the reflector to get a parallel beam of light through which we can see to a longer distance.

Question 9

You are provided with a concave mirror, a convex mirror, a Concave lens and a convex lens. To obtain an enlarged image of an object you can use either

Accepted Answer

The correct answer is option (b), Concave mirror or convex lens. Enlarged images are formed by only concave mirror or convex lens.

Question 10

If the image formed by a spherical mirror for all positions of the object placed in front of it is always erect and diminished, what type of mirror is it? Draw a labelled ray diagram to support your answer.

Accepted Answer

Convex mirror always forms a virtual, erect and diminished image of the object placed at any position in front of the mirror.

Parts of Spherical Mirrors

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Find the size, nature and position of image formed when an object of size $1 c m$ is placed at a distance of $15 c m$ from a concave mirror of focal length $10 c m$ ?

An object is placed at (i) $10 c m$ , (ii) $5 c m$ in front of a concave mirror of radius of curvature $15 c m$ . Find the position, nature and magnification of the image in each case.

Draw a ray diagram to show the formation of image by a concave mirror for an object beyond its center of curvature. State three characteristics of the image.

Which of the following can make a parallel beam of light when light from a point source is incident on it?

Explain why a ray of light passing through the centre of curvature of a concave mirror gets reflected along the same path after reflection.

In torches, search lights and headlights of vehicles the bulb is placed:

You are provided with a concave mirror, a convex mirror, a Concave lens and a convex lens. To obtain an enlarged image of an object you can use either

If the image formed by a spherical mirror for all positions of the object placed in front of it is always erect and diminished, what type of mirror is it? Draw a labelled ray diagram to support your answer.

Parts of Spherical Mirrors

Language

Rate

REVISE WITH CONCEPTS

Basic Terms Related to Image Formation by Spherical Mirror

Terms Related To Spherical Mirrors

QUICK SUMMARY WITH STORIES

Terms Related to Spherical Mirror

Basic Terms Related to Spherical Mirrors

Find the size, nature and position of image formed when an object of size 1cm is placed at a distance of 15 cm from a concave mirror of focal length 10cm?

An object is placed at (i) 10 cm, (ii) 5 cm in front of a concave mirror of radius of curvature 15 cm. Find the position, nature and magnification of the image in each case.

Draw a ray diagram to show the formation of image by a concave mirror for an object beyond its center of curvature. State three characteristics of the image.

Which of the following can make a parallel beam of light when light from a point source is incident on it?

Explain why a ray of light passing through the centre of curvature of a concave mirror gets reflected along the same path after reflection.

In torches, search lights and headlights of vehicles the bulb is placed:

You are provided with a concave mirror, a convex mirror, a Concave lens and a convex lens. To obtain an enlarged image of an object you can use either

If the image formed by a spherical mirror for all positions of the object placed in front of it is always erect and diminished, what type of mirror is it? Draw a labelled ray diagram to support your answer.

Find the size, nature and position of image formed when an object of size $1 c m$ is placed at a distance of $15 c m$ from a concave mirror of focal length $10 c m$ ?

An object is placed at (i) $10 c m$ , (ii) $5 c m$ in front of a concave mirror of radius of curvature $15 c m$ . Find the position, nature and magnification of the image in each case.