# Frank Solutions for Chapter 6A Light- Spherical Mirrors Class 9 Physics ICSE

1. What do you mean by a spherical mirror?

A spherical mirror is a part of a hollow glass sphere silvered on one side.

2. Explain with a suitable diagram, the converging of a parallel beam of light rays by a concave mirror.

The parallel beam of light on reflection by a concave mirror converges at a point on the principal axis, midway between pole and the centre of curvature. This point is called principal focus

3. If the radius of curvature of a concave mirror is 30 cm, what is its focal length?

Focal length = 1/2 of radius of curvature

= 1/2 × 30

= 15cm

4. What do you mean by a focal point?

Focal point is the principle focus of the mirror where a parallel bean of light meets (or appears to meet) after reflection from the mirror.

5. Distinguish between real and virtual images.

Difference between real and virtual images

6. Define the terms;

(i) Pole

(ii) Centre of curvature

(iii) Aperture

(iv) Principal axis

(v) Principal focus

(i) Pole is the centre of the reflecting surface, in this case spherical mirror.

(ii) Centre of curvature is the centre of the imaginary sphere to which the mirror belongs

(iii) Aperture is the distance between the extreme points on the periphery of the mirror.

(iv) Principal axis is the straight line passing through the pole and the centre of curvature.

(v) The principle focus of a spherical mirror may be defined as a point on its principle axis where a beam of light parallel to the principle axis converges to or appears to diverge from after reflection from the spherical mirror.

7. Which mirror has a wider field of view?

Convex mirror has a wider field of view.

8. Give three applications of concave mirrors.

Concave mirrors are used in reflecting microscope, in shaving and make up glasses and in ophthalmoscope.

9. Mention one main application of convex mirrors.

Convex mirrors are used as a rear view mirror in automobiles as it provides a wider view of following traffic.

10. What kind of mirror is used in vehicles to see the traffic following it?

Convex mirror is used in vehicles to see the traffic following it.

11. For what position of an object, a concave mirror forms a real image equal in size to the object?

A concave mirror forms a real image equal in size to the object when the object is kept at centre of curvature, C

12. For what position of an object, a concave mirror forms an enlarged virtual image?

A concave mirror forms an enlarged virtual image when the object is kept between focus, F and pole, P

13. Name the spherical mirror which can produce a real and diminished image of the object.

Concave mirror can produce real and diminished image of the object.

14. What is the focal length of a plane mirror?

The focal length of plane mirror is infinity.

15. Where should an object be placed in front of a concave mirror so as obtain its magnified erect image?

The object should be placed between F and P to obtain its magnified and erect image.

16. How will you determine the focal length of a concave mirror?

Let’s assume the aperture of the mirror to be very small. Let a ray AB of light parallel to the principal axis be incident on the concave mirror at B. the ray makes the angle of incidence, i with the normal BC at B, C being the centre of curvature of the mirror. The ray is reflected along BF with angle of reflection, r so that

<i = <r

In accordance with the laws of reflection. As the incident ray AB is parallel to the principal axis PC, so the reflected ray Bf passes through the principal focus, F. in figure (i)

< ABC = < CBF

But < ABC = alternate < BCF

Therefore < CBF = < BCF

And the ∆FBC is isosceles

BF = FC …(i)

Since the aperture is assumed to be very small, so the point of incidence B is close to P

And BF = PF (approx.) …(ii)

From (i) and (ii)

PF = FC

PF + PF = PF + FC

2PF = PC

Now since PF = f, the focal length of the mirror

And PC = R, the radius of curvature of the mirror

Therefore 2f = R

From here we can determine the focal length of the concave mirror i.e. half of radius of curvature

17. What do you mean by the magnification produced by mirrors?

Linear magnification is defined as the ratio of the height of the image to the height of the object. It is taken to be positive for an image to be virtual and erect and negative when image is real and inverted.

Magnification = height of image/height of object.

18. Write down the SI unit of focal length.

SI unit of focal length is meter.

19. A person in front of a spherical mirror finds his image having a very small head, a fat body and legs of normal size. What are the shapes of three parts of the mirror?

The top mirror is convex mirror, the middle mirror is concave mirror and bottom mirror is a plane mirror.

20. What is the nature of a mirror having a focal length of +15 cm?

The mirror having +15 cm as its focal length is a convex mirror because focal length is taken positive only in case of convex mirror.

21. What is the nature of the mirror having a focal length of -20 cm?

The mirror having -20 cm as its focal length is a concave mirror because focal length is taken negative only in case of concave mirror.

22. When we look into a plane mirror, is the image of our face real or virtual?

When we look into a plane mirror, the image of our face is virtual because the image cannot be obtained on a screen.

23. An object is brought towards a concave mirror. How does the position and size of the image change?

When an object is brought towards the concave mirror, the position of the image moves away from the mirror and the size increases and it remains inverted but at object position between F and P the image is virtual, magnified and erect.

24. In fig. 22, AB is the object, A1B1 is its image. MM‘ is the position of the mirror. Complete the ray diagram and find the position of centre of curvature and focus of mirror. Also, measure the focal length.

A light ray coming from a point on object AB is reflected from the surface of the mirror. When this ray is produced backwards, it passes through the principal focus and the ray which traces its incident path after reflection, when produced backwards, passes through the centre of curvature. These two reflected rays coincide at a point where the image is formed. The image, A’B’ is virtual, erect, and diminished in size.

The focal length was found to be 24 mm

25. In fig. 24, AB is the object, A1B1 is the image and MM‘ is the position of mirror. Complete the ray diagram showing the formation of the image and find the focal length of mirror.

A light ray coming from a point on object AB is reflected from the surface of the mirror, it passes through the principal focus and the other ray passing through the centre of curvature strikes the mirror normally i.e. 90 degree.

Hence it will reflect back. These two reflected rays coincide at a point where the image is formed. The image, A’B’ is real, inverted, and diminished in size. The focal length was found to be 16 mm

26. Complete the following diagrams shown in fig. 26 by drawing the reflected rays.

A light ray when produced backwards passes through principal focus as shown in the problem figure. We draw the normal through centre of curvature at the point of incidence and draw the reflected ray at an angle equal to the angle of incidence thus following the laws of reflection. The reflected ray is parallel to the principal axis. The other ray is reflected at the pole by an angle in accordance with the laws of reflection. These two reflected rays when produced backwards coincide at a point where the image is formed. The image, A’B’ is virtual, erect, and diminished in size

A light ray coming from a point on object AB is reflected from the surface of the mirror, it passes through the principal focus and the other ray passing through the centre of curvature strikes the mirror normally i.e. 90 degree. Hence it will reflect back. These two reflected rays coincide at a point where the image is formed. The image, AB’ is real, inverted, and diminished in size.

27. Complete the following diagrams shown in fig. 27 by drawing the reflected ray for each incident ray.

A light ray when produced backwards passes through principal focus as shown in the problem figure. We draw the normal through centre of curvature at the point of incidence and draw the reflected ray at an angle equal to the angle of incidence thus following the laws of reflection. The reflected ray is parallel to the principal axis. The other ray is passing through the centre of curvature as shown in problem figure. This ray retraces its incident path because it strikes the mirror normally i.e. 90 degrees. These two reflected rays when produced backwards coincide at a point where the image is formed. The image, AB’ is virtual, erect, and diminished in size

A light ray coming from a point on object AB passes through the principal focus and after reflection, it becomes parallel to the principal axis in accordance with laws of reflection and the other ray passing through the centre of curvature strikes the mirror normally i.e. 90 degree. Hence it will reflect back. These two reflected rays coincide at a point where the image is formed. The image, AB’ is real, inverted, and diminished in size.

28. Fig. 28 shows a concave mirror with its pole (P), focus (F) and center of curvature (C). Draw ray diagram to show the formation of image of an object AB by the concave mirror.