Question

an object placed at a distance of 10 metres from the pole of a concave mirror the image observed at 6 cm from the pole calculate the focal length of mirror​

Answer 1

Given :-

Distance of the object = -10 m

Distance of the image = -6 m

To Find :-

The focal length of the mirror.

Analysis :-

Here we are given with distance of the object and the distance of the image.

In order to find the focal length substitute the values given in the questions accordingly using the mirror formula.

Solution :-

We know that,

• u = Distance of the object
• f = Focal length
• v = Distance of the image

$\underline{\boxed{\sf Mirror \ formula=\dfrac{1}{v}+\dfrac{1}{u}=\dfrac{1}{f} }}$

Given that,

Distance of the object (u) = -10 m

Distance of the image (v) = -6 m

Substituting their values,

$\sf \dfrac{1}{f} =\dfrac{1}{-10} +\dfrac{1}{-6}$

$\sf \dfrac{1}{f} =\dfrac{-6-10}{60}$

$\sf \dfrac{1}{f} =\dfrac{-16}{60}$

$\sf f=-3.75 \ m$

Therefore, the focal length of the mirror is -3.75 m.

Answer 2

$\Large\bf{\color{indigo} GiVeN,}$

$\bf\pink{A\:concave\:mirror,}$

• Object distance (u) = -10 m

• Image distance (v) = -6 m

[NOTE ↠ Here both object distance & image distance are negative. Because both object & image are placed in-front of the concave mirror.]

✅ [See the attachment ray diagram.]

$\bf\purple{We\:know\:that,}$

☆ Mirror formula is,

$\red\bigstar\:\:{\green{\boxed{\bf{\color{peru}\dfrac{1}{v}\:+\:\dfrac{1}{u}\:=\:\dfrac{1}{f}\:}}}}$

$\bf\green{Where,}$

• f is the focal length of concave mirror.

$:\implies\:\:\bf{\dfrac{1}{-6}\:+\:\Big(\dfrac{1}{-10}\Big)\:=\:\dfrac{1}{f}\:}$

$:\implies\:\:\bf{-\dfrac{1}{6}\:-\:\dfrac{1}{10}\:=\:\dfrac{1}{f}\:}$

$:\implies\:\:\bf{\dfrac{-5\:-\:3}{30}\:=\:\dfrac{1}{f}\:}$

$:\implies\:\:\bf{\dfrac{-8}{30}\:=\:\dfrac{1}{f}\:}$

$:\implies\:\:\bf{f\:=\:-\dfrac{30}{8}\:}$

$:\implies\:\:\bf\blue{f\:=\:-\:3.75\:m}$

$\Large\bold\therefore$ The focal length of mirror is -3.75 m.