Question 1.
The laws of reflection hold true for
(a) plane mirrors only
(b) concave mirrors only
(c) convex mirrors only
(d) all reflecting surface
Answer:
(d) The laws of reflection holds true for all reflecting surface.
Question 2.
List four characteristics of the images formed by plane mirrors. (Delhi 2015, AI2011)
Answer:
Characteristics of the image formed by a plane mirror are
(i) imagedistanceissameasthatofobjectdistance
(ii) image formed is virtual and erect
(iii) image formed is of the same size as that of the object
(iv) image formed is laterally inverted (left appears right and right appears left).
Question 3.
State the two laws of reflection of light. (Delhi 2011)
Answer:
Laws of reflection of light states that
(i) The angle of incidence is equal to the angle of reflection.
(ii) The incident ray, the reflected ray and the normal to the mirror at the point of incidence all lie in the same plane.
Question 4.
When an object is kept within the focus of a concave mirror, an enlarged image is formed behind the mirror. This image is
(a) real
(b) inverted
(c) virtual and inverted
(d) virtual and erect (2020)
Answer:
(d) When an object is placed between the principal focus and pole of a concave mirror, an enlarged virtual and erect image is formed behind the mirror.
Question 5.
What is the magnification of the images formed by plane mirrors and why? (Delhi 2015)
Answer:
Magnification of images formed by plane mirrors is unity because for plane mirrors, the size of the image formed is equal to that of the object. Question 6.
Draw a labelled ray diagram to show the path of the reflected ray corresponding to an incident ray of light parallel to the principal axis of a convex mirror. Mark the angle of incidence and angle of reflection on it. (AI 2019)
Answer:
Question 8.
An object is placed at a distance of 30 cm in front of a convex mirror of focal length 15 cm. Write four characteristics of the image formed by the mirror. (Delhi 2017)
Answer:
Four characteristics of the image formed by the given convex mirror are :
(i) Virtual
(ii) Erect
(iii) Diminished
(iv) Image is always formed behind the mirror between pole and focus.
Question 9.
An object is placed at a distance of 12 cm in front of a concave mirror of radius of curvature 30 cm. List four characteristics of the image formed by the mirror. (Delhi 2017)
Answer:
Radius of curvature (R) = 30 cm, object distance is 12 cm in front of the mirror. Thus we can say that object is placed between focus and pole. Four characteristics of the image formed by die given concave mirror when object is placed between pole and focus are:
(i) Virtual
(ii) Erect
(iii) Enlarged
(iv) Image is formed behind the mirror
Question 10.
A ray of light is incident on a convex mirror as shown. Redraw the diagram and complete the path of this ray after reflection from the mirror. Mark angle of incidence and angle of reflection on it. (Delhi 2016)
Answer:
Question 11.
Name the type of mirrors used in the design of solar furnaces. Explain how high temperature is achieved by this device. (AI 2016)
Answer:
Concave mirrors are used in the designing of solar furnaces.
When a solar furnace is placed at the focus of a large concave mirror, it focuses a parallel beam of light on the furnace. Therefore, a high temperature is attained at the point after some time.
Question 12.
“The magnification produced by a spherical mirror is -3”. List four informations you obtain from this statement about the mirror/ image. (AI 2016)
Answer:
Negative sign of magnification indicates that the image is real and inverted. Since the image is real and inverted, the mirror is concave and magnification of -3 indicates that the image is magnified.
Question 13.
AB and CD, two spherical mirrors, from parts of a hollow spherical ball with its center at O as shown in the diagram. If arc AB = 12 arc CD, what is the ratio of their focal lengths? State which of the two mirrors will always form virtual image of an object placed in front of it and why? (Foreign 2016)
Answer:
Focal length of a mirror is given by
Focal length = Radiusofcurvature2
Since both the mirrors have same radius of curvature, therefore focal length of the two mirrors will be same, i.e.,
f1f2 = 11
Since virtual image is always formed by convex mirror. The mirror AB will always form virtual image. Question 14.
List two properties of the images formed by convex mirrors. Draw ray diagram in support of your answer. (Foreign 2016)
Answer:
Convex mirrors always form diminished, virtual and erect images.
Question 15. The linear magnification produced by a spherical mirror is +3. Analyze this value and state the (i) type of mirror and (ii) position of the object with respect to the pole of the mirror. Draw a ray diagram to show the formation of image in this case. (Foreign 2016) Answer: Positive value of the magnification indicates that image is virtual and erect. (i) Since the image is magnified, the mirror is concave. (ii) The object is between pole and focus of the mirror as shown
The image produced in second case will be real and inverted.
Question 16.
List four specific characteristics of the images of the objects formed by convex mirrors. (Delhi 2015)
Answer:
Refer to answer 8 Question 17.
Draw a ray diagram to show the path of the reflected ray corresponding to an incident ray which is directed towards the principal focus of a convex mirror. Mark on it the angle of incidence and the angle of reflection. (Delhi 2014)
Answer:
Question 18.
Draw a ray diagram to show the path of the reflected ray corresponding to an incident ray which is directed parallel to the principal axis of a convex mirror, Mark on it the angle of incidence and the angle of reflection. (Delhi 2014)
Answer:
Refer to answer 6 Question 19.
Draw a ray diagram to show the path of the reflected ray corresponding to an incident ray of light parallel to the principal axis of a concave mirror. Mark the angle of incidence and angle of reflection on it. (Delhi 2014)
Answer:
Question 20.
List two possible ways in which a concave mirror can produce a magnified image of an object placed in front of it. State the difference if any between these two images. (AI2014)
Answer:
A concave mirror can produce a magnified image of an object when object is placed:
(1) In between its pole and its focus
(2) In between its focus and its center of curvature.
Difference, between these two images:
The image produced in first case will be virtual and erect.
The image produced in second case will be real and inverted. Question 21.
The image formed by a concave mirror is observed to be virtual, erect and larger than the object. Where should the position of the object be relative to the mirror? Draw ray diagram to justify your answer. (AI 2014)
Answer:
The position of the object should be between P and F
Question 22.
The linear magnification produced by a spherical mirror is +1/3. Analyzing this value state the (i) type of mirror and (ii) position of the object with respect to the pole of the mirror. Draw any diagram to justify your answer. (AI 2014, Foreign 2014)
Answer:
(i) Convex mirror
(ii) Between infinity and the pole of the mirror
Question 23.
The linear magnification produced by a spherical mirror is -1. Analysing this value state the (i) type of mirror and (ii) position of the object with respect to the pole of the mirror. Draw any diagram to justify your answer. (Foreign 2014)
Answer:
(i) Concave mirror because the image is real, inverted.
(ii) Object is placed at C.
Question 24.
The linear magnification produced by a spherical mirror is -1/5. Analysing this value state the (i) type of spherical mirror and (ii) the position of the object with respect to the pole of the mirror. Draw ray diagram to justify your answer. (Foreign 2014)
Answer:
(i) Concave mirror
(ii) Object is placed beyond C.
Question 25.
Draw ray diagrams for the following cases when a ray of light:
(i) passing through centre of curvature of a concave mirror is incident on it.
(ii) parallel to principal axis is incident on convex mirror.
(iii) is passing through focus of a concave mirror incident on it. (2020)
Answer:
(i) Ray of light passing through centre of curvature of concave mirror, after reflection
(ii) Ray of light parallel to the principal axis is incident on a convex mirror after reflection appear to diverge from the principal focus of a convex mirror.
(iii) Ray of light passing through focus of a concave mirror after reflection will emerge parallel
Question 26. A concave mirror is used for image formation for different positions of an object. What inferences can be drawn about the following when an object is placed at a distance of 10 cm from the pole of a concave mirror of focal length 15 cm? (a) Position of the image (b) Size of the image (c) Nature of the image Draw a labelled ray diagram to justify your inferences. (2020) Answer: Given, f = -15 cm, u = -10 cm. Thus the object is placed between the principal focus and pole of the mirror. (a) The position of the image will be behind the mirror. (b) The size of the image will be highly enlarged. (c) The nature of the image will be virtual and erect.
Question 27.
A concave mirror has a focal length of 20 cm. At what distance from the mirror should a 4 cm tall object be placed so that it forms an image at a distance of 30 cm from the mirror? Also calculate the size of the image formed. (AI 2019)
Answer:
Given f = -20 cm v = -30 cm u = ?
Using 1v + 1u = 1f
1u = 1f – 1v = 1−20 – 1−30 = −3+260
⇒ u = -60 cm
∴ Object placed at 60 cm from the mirror.
Also magnification, m = h′h = −vu
⇒ h’ = −(−30)−60 × 4 = -2 cm
∴ The size of the image is 2 cm.
Question 28.
The image of a candle flame placed at a distance of 30 cm from a mirror is formed on a screen placed in front of the mirror at a distance of 60 cm from its pole. What is the nature of the mirror? Find its focal length. If the height of the flame is 2.4 cm, find the height of its image. State whether the image formed is erect or inverted. (Delhi 2017)
Given:
Object distance, u = – 30 cm, image size, h’ = ?
Image distance, v = – 60 cm,
Object size ,h = 2.4 cm,
Focal length, f = ?
Using mirror formula,
1f=1v+1u or 1f=−1−260=−360=−120
or f = – 20 cm
Hence, focal length is 20 cm
Also, magnification, m = h′h = −vu
or, m = (−60)(−30) = -2 or h′h = -2
h’ = – 2 × 2.4 = – 4.8 cm
As the image formed is real, therefore the mirror is concave.
The height of the image is 4.8 cm.
The image formed is enlarged and inverted.
Question 29.
An object 4 cm in height, is placed at 15 cm in front of a concave mirror of focal length 10 cm. At what distance from the mirror should a screen be placed to obtain a sharp image of the object. Calculate the height of the image. (Delhi 2017)
Answer:
Given : object distance, u = -15 cm,
object height, h = 4 cm, focal length f = -10 cm;
Image distance, v = ?
Using mirror formula,
1v+1u=1f⇒1v+1(−15)=1−10⇒1v=115−110
or 1v=10−15150=−5150=−130 or v = -30
In order to obtain a sharp image of the object on the screen, screen should be placed at a distance of 30 cm in front of the mirror.
Also, magnification, m = h′h=−vu
or h′4=−(−30)(−15) or h’ = −(30)×4(15) = -2 × 4
or h’ = -8 cm
Thus, the height of the image is 8 cm. Question 30.
Draw the following diagram in which a ray of light is incident on a concave/convex mirror, on your answer sheet. Show the path of this ray, after reflection, in each case.
Answer:
The path of the rays are shown in figure.
Question 31.
The image of an object formed by a mirror is real, inverted and is of magnification -1. If the image is at a distance of 40 cm from the mirror, where is the object placed? Where would the image be if the object is moved 20 cm towards the mirror? State reason and also draw ray diagram for the new position of the object to justify your answer. (AI 2016)
Answer:
Since the image formed by the mirror is real and inverted, therefore the mirror is concave and magnification of the mirror will be
m = –vu ⇒ -1 = –vu ⇒ v = u
i.e., object and image both are formed at the centre of curvature, i.e., 40 cm from the mirror.
Now, if the object is moved 20 cm towards the mirror, the object will be at the focus of the mirror and therefore the image will be formed at infinity.
Question 32.
The image formed by a spherical mirror is real, inverted and its magnification is -2. If the image is at a distance of 30 cm from the mirror, where is the object placed? Find the focal length of the mirror. List two characteristics of the image formed if the object is moved 10 cm towards the mirror. (AI 2016)
Answer:
Since the image formed is real and inverted, the mirror is concave.
Magnification, m = −vu ⇒ -2 = −vu ⇒ v = 2u
Now, if v = – 30 cm then u = – 15 cm
As focal length of the mirror is
f = uvu+v=−15×−30−15−30=f=450−45 = -10 cm
If the object is shifted 10 cm towards the mirror, then the object is between principal focus and the optical centre and the image formed will be virtual and erect.
Question 33.
If the image formed by mirror for all positions of the object placed in front of it is always virtual and diminished, state the type of the mirror. Draw a ray diagram in support of your answer. Where are such mirrors commonly used and why? (Foreign 2016, AI 2015)
Answer:
Refer to answer 7.
Convex mirrors are widely used as rear view mirrors in cars, motorcycles etc. It produces an erect image that is smaller in size than the object hence giving a wide view. Question 34.
To construct a ray diagram we use two rays of light which are so chosen that it is easy to determine their directions after reflection from the mirror. Choose these two rays and state the path of these rays after reflection from a concave mirror. Use these two rays to find the nature and position of the image of an object placed at a distance of 15 cm from a concave mirror of focal length 10 cm. (Delhi 2015, AI 2012)
Answer:
We use two rays of light, one passing through the center of curvature of a concave mirror, and another is parallel to the principal axis. After reflection, the ray passing through the center of a concave mirror is reflected back along the same path and the ray parallel to the principal axis will pass through the principal focus.
u = -15 cm, f= -10 cm
From ray diagram, v = -30 cm, i.e., beyond C Nature of image is real, inverted and magnified. Question 35.
Draw a ray diagram to show the path of the reflected ray in each of the following cases. A ray of light incident on a convex mirror :
(a) strikes at its pole making an angle 0 from the principal axis.
(b) is directed towards its principle focus.
(c) is pardllel to its principal axis. (Foreign 2015)
Answer:
(b) Refer to answer 17.
(c) Refer to answer 6.
Question 36.
A spherical mirror produces an image of magnification -1 on a screen placed at a distance of 50 cm from the mirror.
(a) Write the type of mirror.
(b) Find the distance of the image from the object.
(c) What is the focal length of the mirror?
(d) Draw the ray diagram to show the image formation in this case. (Delhi 2014, AI 2014)
Answer:
(a) Concave mirror
(b) Magnification, m = –vu or v = u
∴ Distance of the image from the object is, v – u = 0
(c) As the image is formed at centre of curvature i.e., v = R.
∴ focal length of the mirror, f = −502 = -25 cm
(d) Refer to answer 23(ii).
Question 37.
A spherical mirror produces an image of magnification -1 on a screen placed at a distance of 40 cm from the mirror.
(i) Write type of mirror.
(ii) What is the nature of the image formed?
(iii) How far is the object located from the mirror?
(iv) Draw the ray diagram to show the image formation in this case. (Delhi 2014)
Answer:
(i) This is a concave mirror.
(ii) The image is real and inverted and of same size.
(iii) As m = – 1
∴ m = –vu ⇒ -1 = −vu ⇒ u = v
Hence, object is located at centre of curvature i.e., at distance of 40 cm from the pole of the mirror,
(iv) Refer to answer 23(ii).
Question 38.
A spherical mirror produces an image of magnification -1.0 on a screen placed at a distance of 30 cm from the pole of the mirror.
(i) Write the type of mirror in this case.
(ii) What is the focal length of the mirror?
(iii) What is the nature of the images formed?
(iv) Draw the ray diagram to show the image formation in this case. (Delhi 2014)
Answer:
(i) The mirror is concave mirror.
(ii) Distance the image from the mirror = – 30 cm
Magnification, m = −vu
Here m = – 1 and v = – 30 cm
-1 = –(−30)u
∴ u = – 30 cm
As v = u, object is placed at centre of curvature. Therefore, focal length of the mirror,
f = −302 = – 15 cm
(iii) Image formed is real and inverted and of the same size of the object.
(iv) Refer to answer 23(ii). Question 39.
A student wants to project the image of a candle flame on a screen 48 cm in front of a mirror by keeping the flame at a distance of 12 cm from its pole.
(a) Suggest the type of mirror he should use.
(b) Find the linear magnification of the image produced.
(c) How far is the image from its object?
(d) Draw ray diagram to show the image formation in this case. (AI 2014)
Answer:
(a) Concave mirror
(b) Linear magnification,
m = −vu = −(−48)−12 = -4
(c) The distance between the image and the object
= 48 – 12 = 36 cm
Question 40.
A student wants to obtain an erect image of an object using a concave mirror of 12 cm focal length. What should be the range of distance of the candle flame from the mirror? State the nature and size of the image he is likely to observe. Draw a ray diagram to show the image formation in this case. (Foreign 2014)
Answer:
To obtain an erect image, the object is placed in between pole and the focus of the concave mirror. So range of distance of the candle llame from the mirror is in between 12 cm.
Nature of the image = Virtual and erect.
Size of the image = Enlarged
Question 41.
A student wants to obtain an erect image of a candle flame using a concave mirror of focal length 15 cm. What should be the range of distance of the candle flame from the mirror?
State the nature and size of the image he is likely to observe. Draw a ray diagram to show the image formation in this case. (Foreign 2014)
Answer:
To obtain an erect image of an object, the object should be placed in between pole and focus. Range of distance of the candle flame from the mirror is in between 15 cm.
Nature of the image = Virtual and erect
Size of the image = Enlarged
For ray diagram, refer to answer 40.
Question 42.
A student has a concave mirror of 20 cm focal length and he wants to see an erect image of his face in the mirror. What should be the range of distance of the mirror from his face? State the nature and size of the image he is likely to observe. Draw a ray diagram to justify your answer. (Foreign 2014)
Answer:
Focal length of a concave mirror = 20 cm Range will be in between 20 cm.
Nature of the image = Virtual and erect
Size of the image = Enlarged
For ray diagram, refer to answer 40.
Question 43.
Mention the types of mirrors used as (i) rear view mirrors, (ii) shaving mirrors. List two reasons to justify your answer in each case. (Delhi 2013, Delhi 2012)
Answer:
(i) Convex mirror is used as rear view mirror because
(a) it gives erect image.
(b) it gives diminished image thus provides wider view of traffic behind the vehicle.
(ii) Concave mirror is used as shaving mirror because
(a) it gives erect image when mirror is close to the face.
(b) it gives enlarged image of the face so that a person can shave safely. Question 44.
Calculate the magnification of the image of an object placed perpendicular to the principal axis of a concave mirror of focal length 15 cm. The object is at a distance of 20 cm from the mirror. (Delhi 2013)
Answer:
Given, focal length of concave mirror,
f = -15 cm
Object distance, u = -20 cm
Image distance, v = ?
Using mirror formula,
Using magnification formula,
m = –vu = -(−60−20) or m = -3
So, the magnification, m = -3.
Question 45.
To construct ray diagram we use two light rays which are so chosen that it is easy to know their directions after reflection from the mirror. List these two rays and state the path of these rays after reflection. Use these rays to locate the image of an object placed between centre of curvature and focus of a concave mirror. (AI2012)
Answer:
A ray parallel to the principal axis, after reflection, will pass through the principal focus in case of a concave mirror or appear to diverge from the principal focus in case of a convex mirror. A ray passing through the centre of a curvature of a concave mirror or directed in the direction of the centre of curvature of a convex mirror, after reflection, is reflected back along the same path. The light rays come back along the same path because the incident rays fall on the mirror along the normal to the reflecting surface.
Question 46.
State the types of mirrors used for (i) headlights and (ii) rear view mirrors, in motorcycles. Give reason to justify your answer in each case. (AI 2012)
Answer:
(i) Concave mirrors are used in headlights of cars to get powerful beams of light.
(ii) Convex mirrors are used as rear-view mirrors of vehicle to get a wider field of view and and erect image of traffic behind. Question 47.
An object is placed between infinity and the pole of a convex mirror. Draw a ray diagram and also state the position, the relative size and the nature of the image formed. (AI 2011)
Answer:
Position: Image is formed between pole and principal focus of the mirror.
Relative size : Image formed is diminished.
Nature : Image formed is virtual and erect. Question 48.
With the help of a ray diagram explain why a convex mirror is preferred for rear view mirrors in the motor cars. (Foreign 2011)
Answer:
Convex mirror is preferred for rear view mirrors in motor cars because no matter where the object is located in front of convex mirror, it always gives erect and diminished image of the object, so that driver is able to see the large traffic view in small area and the image is erect. This can be interpreted from the following diagram.
Question 49.
An object 4.0 cm in size, is placed 25.0 cm in front of a concave mirror of focal length 15.0 cm.
(i) At what distance from the mirror should a screen be placed in order to obtain a sharp image?
(ii) Find the size of the image.
(iii) Draw a ray diagram to show the formation of image in this case. (2020)
Answer:
(i) Given, h = 4 cm,
u = -25 cm (concave mirror), f = -15 cm
Using mirror formula,
Thus, the image is real and inverted.
Question 50.
(a) A concave mirror of focal length 10 cm can produce a magnified real as well as virtual image of an object placed in front of it. Draw ray diagrams to justify this statement,
(b) An object is placed perpendicular to the principal axis of a convex mirror of focal length 10 cm. The distance of the object from the pole of the mirror is 10 cm. Find the position of the image formed. (2020)
Answer:
(a) A magnified real image is produced in a concave mirror when the object is placed between principal focus and center of curvature.
A magnified virtual image is produced in a concave mirror when the object is placed between the pole and the principle focus of the mirror
(b) Given, f = +10 cm (convex mirror) and u = -10 cm
From mirror formula,
Question 51.
(a) A security mirror used in a big showroom has radius of curvature 5 m. If a customer is standing at a distance of 20 m from the cash counter, find the position, nature and size of the image formed in the security mirror.
(b) Neha visited a dentist in his clinic. She observed that the dentist was holding an instrument fitted with a mirror. State the nature of this mirror and reason for its use in the instrument used by dentist. (2020)
Answer:
(a) Given radius of curvature of the mirror,
R = 5 m
∴ Focal length, f = R/2 = 2.5 m (convex mirror) and u = -20 m
From mirror formula,
1f=1v+1u or 1v=1f−1u
= 12.5−1−20=−20−2.5−20×2.5
∴ v = 2.22 m
Thus, the image is formed 2.22 m behind the mirror. The image is diminished, virtual and erect.
(b) Concave mirrors are used by dentist. Dentist use it as it is a converging mirror and when used at close range forms a highly enlarged, virtual and erect image of the object.
Question 52.
(a) To construct a ray diagram we use two rays which are so chosen that it is easy to know their directions after reflection from the mirror. Use these two rays and draw ray diagram to locate the image of an object placed between pole and focus of a concave mirror.
(b) A concave mirror produces three times magnified image on a screen. If the objects placed 20 cm in front of the mirror, how far is the screen from the object? (Delhi 2017)
Answer:
(a) Two lights rays whose path of reflection are priorly known are :
(i) When the incident ray passes through the centre of curvature of a concave mirror, it gets reflected in the same path.
(ii) When the ray is incident obliquely to the principal axis, towards the pole of mirror, it gets reflected back by making equal angles with the principal axis (laws of reflections). Suppose an object is placed between focus and pole of the concave mirror. Then by using the above two rays, the image of the object can be located as
Image formed is virtual, erect, magnified and it is formed behind the mirror.
(b) Given : Magnification, m = – 3
Object distance, u = – 20 cm
Magnification, m = −vu or -3 = −v−20
or v = -60 cm
The screen is placed in front of the mirror at a distance of 60 cm from the pole.
Thus, the screen is placed 40 cm (= 60 cm – 20 cm) away from the object. Question 53.
(a) If the image formed by a mirror for all positions of the object placed in front of it is always diminished, erect and virtual, state the type of the mirror and also draw a ray diagram to justify your answer. Write one use such mirrors are put to and why?
(b) Define the radius of curvature of spherical mirrors. Find the nature and focal length of a spherical mirror whose radius of curvature is +24 cm. (AI2017)
Answer:
(a) If the image formed by a mirror for all positions of the object placed in front of it is always diminished, erect and virtual then the mirror is convex mirror.
The ray diagrams for the formation of image by a convex mirror for the first position when the object is at infinity and the second position when the object is at a finite distance from the mirror are shown.
Use of Convex Mirrors
Convex mirrors are commonly used as rear-view (wing) mirrors in vehicles because they always give an erect, though diminished image. Also, they have a wider field of view as they are curved outwards. Thus, convex mirrors enable the driver to view a large area.
(b) Radius of Curvature: The radius of the sphere of which the reflecting surface of a spherical mirror forms a part, is called the radius of curvature of the mirror. It is represented by the letter R.
∵ The radius of curvature is equal to twice the focal length.
∴ R = 2f
If R = +24 cm ∴ f = R2 = 242 = 12 cm
Since the radius of curvature is positive, the mirror is convex mirror. Hence the nature of the image is virtual and erect. Question 54.
(a) Define the following terms in the context of spherical mirrors:
(i) Pole
(ii) Centre of curvature
(iii) Principal axis
(iv) Principal focus
(b) Draw ray diagrams to show the principal focus of a
(i) Concave mirror (ii) Convex mirror
(c) Consider the following diagram in which M is a mirror and P is an object and Q is its magnified image formed by the mirror.
State the type of the mirror M and one characteristic property of the image Q. (Delhi 2016)
Answer:
(a) (i) Pole : The center of the reflecting surface of a spherical mirror is a point called the pole. It lies in the surface of the mirror and its represented by the letter P.
(ii) Centre of curvature: The reflecting surface of a spherical mirror is a part of a sphere which has a center. This point is called the center of curvature of spherical mirror and is represented by the letter C.
(iii) Principal axis : An imaginary line passing through the pole and the center of curvature of a spherical mirror and normal to the mirror at its pole is called principal axis.
(iv) Principal focus : Incident rays parallel to principal axis, after reflection either converge to as appear to diverge from a fixed point on the principal axis known as principal focus of the spherical mirror.
(c) The object is placed between focus and pole of the mirror and a magnified image is formed behind the mirror.
∴ The mirror is concave and image formed is virtual and erect.
Question 55.
It is desired to obtain an erect image of an object, using concave mirror of focal length of 12 cm.
(i) What should be the range of distance of a , object placed in front of the mirror?
(ii) Will the image be smaller or larger than the object? Draw ray diagram to show the formation of image in this case.
(iii) Where will the image of this object be, if it is placed 24 cm in front of the mirror? Draw ray diagram for this situation also to justify your answer.
Show the positions of pole, principal focus and the center of curvature in the above ray diagrams. (AI2016)
Answer:
Given : focal length of the concave mirror f = 12 cm
(i) If the object is placed between the pole and focus of the concave mirror, then the image formed is virtual and erect. Inheritor, the range of distance of the object should be 0 < u <. 12 cm. (ii) The image formed will be enlarged as shown below.
(iii) If the object is placed 24 cm in front of the mirror i.e., at the center of the curvature then the image will also be formed at the center of the curvature.
