Solution-Class 9-Science-Chapter-11-Reflection of Light-Maharashtra Board

i.Torch light: In a torch light, the source of light is placed at the focus of the concave mirror to obtain a parallel beam of light.
ii. Projector lamp:  In a projector lamp, the source of light is placed at the centre of curvature of the concave mirror.
iii. Flood light: Here the source of light is placed just beyond the centre of curvature of the concave mirror.

Concave mirror is also known as converging mirror because of its ability of focus the parallel rays at a single point anywhere on its focal plane.

• When rays of light coming from a distant object or source such as the sun and parallel to the principal axis are incident on a concave mirror, after reflection, they converge to a single point (focus ). Thus, a concave mirror is a focusing mirror.
• This results in concentration of heat of the sunlight at that point. Hence, concave mirrors are used in solar devices.

• When an object is kept in front of a convex mirror, we get an erect and diminished image of the object.
• Thus, the convex mirror fitted by the side of a car driver, enables him to get an erect, clear and complete view of the vehicles coming from behind. Hence, a convex mirror is used as a rear-view mirror in a Car.

• The rays from the Sun are parallel. When these rays fall on the concave mirror, they are converged to a single point on the focal plane of the mirror.
• Thus a lot of heat is produced at that point.
• If a paper is placed at that point to get the image of the Sun, the paper gets burnt because of huge amount of heat of the sunlight concentrated at that point

When spherical mirror breaks, their nature does not change because there is no change in the nature of the reflecting surface and radius of the curvature. This means if a concave mirror breaks into pieces, the pieces will act as concave mirrors only. Same happens in case of convex mirrors.

Sign Conventions for spherical Mirrors:

According to the Cartesian sign convention, the pole of a spherical mirror is taken as the origin and principal axis is taken as the X-axis of the frame of references.

(1) Objects are always placed to the left of the mirror i.e. light must fall on the mirror from left to right.

(2) All distances are measured from the pole of the mirror.

(3) Distances along the direction of the incident ray (along positive x- axis) are taken as positive, while distances along the direction of the reflected ray (along negative x-axis) are taken as negative.

(4) Heights measured perpendicular to and above the principal axis (along positive y-axis) are taken as positive.

(5) Heights measured perpendicular to and below the principal axis (along negative y-axis) are taken as negative.

These sign conventions can also represented in the following diagram

(I) Object between the focus (F) and the pole (P)

In this case, the image is formed behind the mirror. This image is virtual, erect and magnified.

(II) Object is at the focus (F)

In this case, the image is formed at infinity. This image is real, inverted and highly enlarged.

(III) Object between the centre of curvature (C) and focus (F)

In this case, the image is formed behind the centre of curvature. This image is real, inverted and magnified.

(IV) Object is at the centre of curvature

In this case, the image is formed at the centre of curvature. This image is real, inverted and of the same size as the object.

(V) Object is beyond the centre of curvature

In this case, the image is formed between the focus (F) and the centre of curvature (C). This image is real, inverted and diminished.

(VI) Object is at infinity

The light rays coming from infinity are parallel. When parallel light rays are incident on the reflecting surface of a concave mirror, they tend to meet at its focus after reflection.

In this case, the image is formed at the focus, and is point-sized. It is real, inverted and highly diminished.

Given, Concave mirror
h₁ = 7 cm
u = −25 cm
f = −15 cm
v=?

h₂=?

(i) As the image to be obtained on a screen, it must be real image

Now,  using mirror formula, we have

1/f = (1/v)+(1/u)

∴ 1/v =(1/f)-(1/u)=(1/-15)-(1/-25) = -2/75

= -37.5 cm
The screen should be placed at a distance of 37.5 cm in front of the concave mirror. 
Now, using magnification formula, we have
h₂/h₁= -(v/u)

∴ h₂ = -h₁(v/u)

∴ h₂ = -7(-37.5/-25)= -7x1.5= -10.5cm

The size (height) of the image = -10.5 cm

 Minus sign shows image is inverted

Given : Convex mirror,  f = 18 cm
h₂ = h₁/2

M= h₂/h₁ = -(v/u) =1/2
∴ v= -(u/2)   …… (i)

(1/v) + (1/u) = 1/f

∴ (1/-(u/2)) + (1/u) = 1/f  …. from eq (i)

∴ (1/u)(1-2) = 1/f

∴ -(1/u) = 1/f

∴ u = -f =-18cm
Hence, the object is kept at 18cm in front of the mirror

Given: Concave mirror, h₁= 10cm, f = -10cm, u = -20cm, h₂ = ?

(1/v) + (1/u) = 1/f

∴ 1/v = (1/f)-(1/u)

∴ u/v = (u/f)-1 = (-20/-10)-1 = 2-1 = 1

∴ u/v = 1

M = h₂/h₁ = -(u/v)

∴ h₂ = -(u/v) x h₁ = -1xh1 = -1x10 = -10cm

Therefore, the length of the image =  10 cm (….minus sign not considered)

Let us name the mirrors as M₁, M₂ and M₃ as shown below.

From the figure, we see that

• pole (P) is not common 
• centre of curvature (C) is common
• principal axis (PA) is not common
• The centre of curvature is the same as the centre of the sphere.
• Similarly the radius of curvature is the same as the radius of the sphere.

Why the pole and the principal axis cannot be common can be seen from the definitions/figure of these terms