An object 1 cm high produces a real image 1 5 cm high, when placed at a distance of 15 - Science -

Question

An object 1 cm high produces a real image 1 5 cm high, when
placed at a distance of
15 cm from a concave mirror Calculate : (i) the position of
the image, (ii) focal length
of the concave mirror

Rosella Rapunzel · Answer

Given :
Object height, h = 1 cm
Image height, h' = 1 5 cm
Object distance, u = -15 cm
To Find :
Position of the image, v
Focal length of the mirror, f
Solution :
Magnification, m = h' / h = - v /
u
h' u / h = v
-v = (1 5)(-15) / 1
-v = -22 5
v = 22 5 cm
As the image is positive, it is a virtual and erect
image Therefore, the image is formed at a distance of 22 5 cm
behind the mirror
1/v + 1/u = 1/f
1/f = 1 / 22 5 + 1 / (-15)
1/f = 1 / 22 5 - 1 / 15
1/f = (15 - 22 5) / 337 5
1/f = -7 5 / 337 5
f = 337 5 / -7 5
f = -45 cm
Therefore, the focal length of the mirror is 45
cm
Hope this helps u

An object 1 cm high produces a real image 1.5 cm high, when placed at a distance of 15 cm from a concave mirror. Calculate : (i) the position of the image, (ii) focal length of the concave mirror.

An object 1 cm high produces a real image 1.5 cm high, when placed at a distance of

15 cm from a concave mirror. Calculate : (i) the position of the image, (ii) focal length

of the concave mirror.