Question

a 10 mm long awl pin is placed vertically in front of concave mirror.a 5mm long image of the awl pin is formed at 30cm in front of mirror . calculate focal length

Answer 1

m= h'/h= -v/u

5/10=-30/u

u=-300/5

u=-60cm

1/f=1/v+1/u

1/f = 1/-30 + 1/-60

1/f = -2-1/60

1/f=-3/60

1/f=-1/20

f=-20cm

Therefore the focal length of the concave mirror is 20 cm front of the mirror

Answer 2

Given that,

Size of an awl pin, h = 10 mm

Size of the image formed of an awl pin, h' = 5 mm

Image distance from the mirror of an awl pin, v = -30 cm (in front of the mirror)

To find,

The focal length of the mirror.

Solution,

We can find the object distance using the formula of magnification such that,

$\dfrac{h'}{h}=\dfrac{-v}{u}$

u is the object distance

$u=\dfrac{-vh}{h'}\\\\u=\dfrac{-30\ cm\times 10\ mm}{5\ mm}\\\\u=-60\ cm$

Let f is the focal length of the mirror. Using mirror's formula we get :

$\dfrac{1}{v}+\dfrac{1}{u}=\dfrac{1}{f}\\\\\dfrac{1}{-30}+\dfrac{1}{(-60)}=\dfrac{1}{f}\\\\f=-20\ cm$

So, the focal length of the mirror is 20 cm.