Question

At what distance from a convex mirror of focal length 2.5 m should
a boy stand so that his image has a height equal to half the original
height? The principal axis is perpendicular to the height.
(a)1.25 m from the mirror
(b)2.5 m from the mirror
0 (c)5.0 m from the mirror
(d)7.5 m from the mirror​

Answer 1

Answer:

Magnification=height of the image/height of the object=-image distance/object distance

Let the actual height be x

=

x

(

2

x

)

=

2

1

2

1

=

u

−v

Usingsignconverstion,

2

1

=

u

v

u=2v

That is object distance is twice the image distance.

So, the object should be placed at the center of curved and the image will be formed at focus.

Object should be placed at center of curvature 2(2.5)=5cm

The image will be formed at focus =2.5 cm

Answer 2

Magnification=height of the image/height of the object=-image distance/object distance
Let the actual height be x
=
x
(
2
x
​
)
​

=
2
1
​

2
1
​
=
u
−v
​

Usingsignconverstion,
2
1
​
=
u
v
​

u=2v
​

That is object distance is twice the image distance.
So, the object should be placed at the center of curved and the image will be formed at focus.
Object should be placed at center of curvature 2(2.5)=5cm
The image will be formed at focus =2.5 cm

Hope it helps!!