Kerala Syllabus Class 8 Basic Science: Chapter 12 Spherical Mirrors - Questions and Answers
Std 8: Physics: Chapter 12: Spherical Mirrors: Questions and Answers
♦ Making a mirror using a cardboard.
Experiment
A silver paper (mirror sticker) has been neatly stuck on a piece of cardboard as in the picture. Doesn’t it look like a mirror? Can you see your face in it?
Fig. 12.3 - Reflecting surface bends outward.
Observation: An erect and small image is seen
Fig. 12.4 - Reflecting surface bends inward.
Observation: Very close objects are seen as big and erect. Far objects are seen small and inverted.
♦ Shall we tabulate the observations?
| Shape of the sheet | Characteristics of the image |
|---|---|
| Flat | Flat, no size difference. |
| Bend outward | erect and small |
| Bend inward | Very close objects are seen as big and erect. Far objects are seen small and inverted. |
♦ Let’s now try another activity. Take a clean steel spoon and observe your face on its both sides.
• How does the image appear on the outer side of the spoon?
On the outer side of the spoon small and erect image is seen.
• What about the inner side?
On the inner side of the spoon small and inverted image is seen.
| A smooth curved surface can also form images like a plane surface. |
|---|
Take the lid off an ice cream ball and stick mirror paper on the inner side of it. Hold it facing the sun and reflect the light rays onto a wall.
Observation: The reflected light rays converge at a point.
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Repeat the activity by sticking mirror paper on the outer surface.
Observation: The light rays get diverged cannot be converged at a point.
♦ Spherical Mirrors
Mirrors whose reflecting surface forms a part of a sphere are called spherical mirrors.
♦ Concave mirrors
Spherical mirrors with a reflecting surface curved inward are called concave mirrors.
♦ Convex mirrors
Spherical mirrors with a reflecting surface curved outward are called convex mirrors.
♦ Let us now get familiar with some terms related to spherical mirrors.
♦ Centre of curvature (C)
The centre of the sphere of which the mirror is a part is called the centre of curvature. It is represented by the letter C.
♦ Radius of curvature (R) CP, CB, and CA
Radius of the sphere from which the mirror is formed. This is the distance from the centre of curvature to the reflection surface of the spherical mirror. It is always perpendicular to the mirror's reflecting surface.
♦ Aperture
The diameter of the circular reflecting surface of a spherical mirror is called the Aperture.
♦ Pole (P)
The midpoint of the reflecting surface is called the Pole (P).
♦ Principal axis
The imaginary line connecting the centre of curvature and the pole of the mirror is called the principal axis.
♦ Reflection in Spherical Mirrors
♦ Activity
Mark the centre of a concave mirror using a sketch pen. Place the mirror halfway inserted into a cardboard piece, as shown in the figure. Stick a printed image of a protractor in front of the mirror.
Draw a straight line to the mirror’s centre. This is the principal axis. Now, shine a laser torch at a fixed angle onto the mirror and observe the reflected ray. Try to trace the path of the reflected ray.
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| SI No | Angle of incidence (i) Degree | Angle of reflection (r) Degree |
|---|---|---|
| 1 | ∠ AOC = 30 | ∠ BOC = 30 |
| 2 | ∠ DOC = 40 | ∠ EOC = 40 |
| 3 | ∠ FOC = 60 | ∠ GOC = 60 |
♦ Repeat this experiment using a convex mirror.
| SI No | Angle of incidence (i) Degree | Angle of reflection (r) Degree |
|---|---|---|
| 1 | ∠ AOC = 30 | ∠ BOC = 30 |
| 2 | ∠ DOC = 40 | ∠ EOC = 40 |
| 3 | ∠ FOC = 60 | ∠ GOC = 60 |
Inference: In spherical mirrors, the angle of incidence is equal to the angle of reflection.
♦ Concave mirror
Hold a concave mirror facing the sun on a sunny day.
All the reflected rays converge to a single point. That point is the focus of the mirror. The focus of a concave mirror is real.
♦ Principal focus of concave mirror
In a concave mirror, the light rays that fall parallel to the principal axis pass through a particular point on the principal axis after reflection. This point is called the principal focus of the concave mirror.
Principal focus of convex mirror
Stick a white paper on a cardboard. Cut a slit and place a convex mirror
partially inserted into the slit. Mark the position of the pole and draw a
perpendicular from that point on the paper to represent the principal axis.
♦ The principal focus of a convex mirror is virtual. Why?
The focus of a convex mirror is virtual, because it cannot be caught on a screen.
♦ Focal Length
In a spherical mirror, the distance from the pole to the principal focus is called the focal length. Its SI unit is metre (m).
For a spherical mirror with a small aperture, the focal length (f) will be half of its radius of curvature (R).
f = R/ 2 Or R = 2f
♦ What would be the radius of curvature of a concave mirror with a focal length of 40 cm?
f = 40 cm
R = 2f = 2 X 40 cm = 80 cm
♦ Image Formation in Spherical Mirrors
♦ We already know about the images formed by plane mirrors. What are their characteristics?
• Erect
• Virtual
• Same size
♦ There are two types of images: real images and virtual images.
Real images are those that can be caught on a screen.
Virtual images are those that cannot be caught on a screen.
♦ If an object is very far away, the image formed by a concave mirror will be at the principal focus of the mirror. Are the images formed by a concave mirror always like this? Let's try an experiment.
Draw a straight line on a table as shown in the picture.
Measuring the distance from the mirror, mark the principal focus and centre of curvature on the line. Now, let's place a lit candle on the straight line. Try to arrange a screen in front of the mirror in such a way that a clear image is obtained.
• At what position is the screen placed to get a clear image?
When the screen is in front of the mirror, between the F and C.
• What are the characteristics of the image?
Real, inverted and small image.
♦ Complete the table given below
♦ Are the same types of images formed in a convex mirror? Try this experiment using a convex mirror.
• Can you see the image?
• Can you project it on a screen?
The image cannot be captured on the screen.
♦ Now, write down the characteristics of the image formed.
• Erect
• Small
• Virtual
A convex mirror always forms a small and erect image. This will be a virtual image. The image will always be between the principal focus and the pole.
♦ Complete the diagrams given below by drawing the normal and the path of the reflected rays.
♦ We know that the position and size of the image vary according to the position of the object, don't we? Let's look at the image formation when the object is placed at different positions (Textbook Page: 213, 214).
1. Object is at infinity
Here, the light ray comes parallel to the principal axis. After reflection, it passes through the principal focus. So, the image is formed at the principal focus itself.
Characteristics of the image:
• Inverted
• Smaller than the object
• Real
2. Object beyond C
Position of the image between F and C.
Characteristics of the image
• Inverted
• Smaller than the object
• Real
3. Object at C
Position of the image - at C
Characteristics of the image
• Inverted
• Same size
• Real
4. Object between C and F
Position of the image - beyond C
Characteristics of the image
• Inverted
• Big
• Real
5. Object at F
Reflected rays are parallel. So there is no image.
6. Object between F and P
Position of the image - Behind the mirror
Characteristics of the image
• Inverted
• Big
• Real
A Concave mirror forms big, small, same size, erect, inverted, real and virtual images.
♦ Image Formation by Convex Mirror
Convex mirrors always form virtual images that are smaller than the object.
♦ Discuss the characteristics of real and virtual images and complete the table given below.
| Real Image | Virtual Image |
|---|---|
| Inverted | Erect |
| Formed in front of the mirror | Formed behind the mirror |
♦ Magnification
The ratio of the height of the image to the height of the object is called magnification.
h₁ - height of the image
h₀ - height of the object
While calculating magnification, measurements above the principal axis should be considered positive and measurements below the principal axis should be considered negative.
♦ Uses of Concave Mirrors
1. Concave mirrors in solar thermal power plants:
Rays of light incident parallel to the principal axis pass through the principal focus after reflection. Hence a lot of heat is generated at this point due to the concentration of energy. This heat can be used to convert water into steam and generate electricity from it. Such power stations are operating in Rajasthan, India.
2. If an object is placed between the principal focus and the pole of a concave mirror, an erect and enlarged virtual image is formed. The following are made using this special feature:
• Shaving mirror
• Makeup mirror
• Mirror used by dentists
3. The path of light rays emitted from the principal focus of a concave mirror travels parallel to the principal axis. We use this property in flashlights and vehicle headlights.
♦ Uses of Convex Mirrors
1. Rear/side view mirror: Convex mirrors are used in vehicles for rear view. It always forms erect and small virtual images. While using convex mirrors, we get more field of view than from a plane mirror.
2. By placing a large convex mirror at the sharp turns of the roads, we can see vehicles coming from beyond the curves and thus reduce accidents.
3. Convex mirrors are often used as reflectors in street lamps.
♦ Why is "OBJECTS IN THE MIRROR ARE CLOSER THAN THEY APPEAR" written on the rearview mirrors of vehicles?
A convex mirror always forms a small and erect image. Therefore, the driver who sees the image in the rearview mirror gets the feeling that the vehicles coming from behind are at a great distance. This can cause accidents. That is why "OBJECTS IN THE MIRROR ARE CLOSER THAN THEY APPEAR" is written on the rearview mirrors of vehicles.
Let’s Assess
1. A concave mirror has a focal length of 30 cm. Find out its radius of curvature.
Answer:
f = 30 cm R = 2f = 2 X 30 = 60 cm
2. OA is a ray incident obliquely on a concave mirror. Draw and mark the path of its reflected ray. Write on what basis you marked like this.
Answer:
angle of incidence = angle of reflection
i = r
3. Write what type of spherical mirrors should be used to obtain images with the following characteristics:
a. Real, smaller than the object
b. Virtual, smaller than the object
c. Real, larger than the object
d. Virtual, larger than the object
Answer:
a. Concave
b. Convex
c. Concave
d. Concave
4. Observe the picture.
b) If the distance of the object from the mirror was 30 cm and an image of the same size as the object was obtained on the screen, what is the focal length of the mirror?
Answer:
a) h₀ = 6 cm, h₁ = ?
m = h₁ / h₀ = ⁻⁶⁄₃ = ⁻2 cm
h₁ / h₀ = m
h₁ / 6 = ⁻2
∴ h₁ = 6 X ⁻2 = ⁻12 cm
height of the image = 12 cm
b) Object is at 2F (C)
2F = 30 cm
f = 15 cm
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