A pencil of length 10 cm lies across the principal axis of a concave mirror having a focal length of 20cm. The pencils tip is towards the focus such that the midpoint of the pencil lies on the centre of curvature. Find the magnification of the image formed.(the height of the pencil is 0 cm a it is horizontaly placed)
Answers
Given info : A pencil of length 10 cm lies across the principal axis of a concave mirror having a focal length of 20cm. The pencils tip is towards the focus such that the midpoint of the pencil lies on the centre of curvature.
To find : the magnification of the image formed.
Solution : this can be solved by assuming there are two points separated 10 cm from each other. and find image each of them after at we get final image of required object.
Let's do it.
here, u = -35 , f = - 20cm
using formula, 1/v + 1/u = 1/f
⇒1/v = 1/f - 1/u = 1/-20 - 1/-35
⇒1/v = (-7 + 4)/140 = -3/140
v = -140/3 cm = -46.67 cm
Again, u' = -45cm, f = -20cm
1/v' = -1/20 + 1/45 [ I hope you understand how I got it ]
= (-9 + 4)/180 = -5/180 = -1/36
v' = -36 cm
So, size of image, V = |v' - v| = 10.67 cm
As image form left side of concave mirror, V = -10.67 cm
Now magnification = - v/u
= -(-10.67)/10 = +1.067
Therefore the magnification of pencil would be 1.067
