Question

A 2.5cm candle is placed 12cm away from a convex mirror of focal length 30cm.give the location of the image and magnification

Answer 1

Given :

• Height of candle (ho) = 2.5cm
• Distance of candle from mirror (u) = +12cm
• Focal lenght of mirror (f) = +30cm

To Find :

• Location of image
• Magnification

Formula Used :

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

$\bullet\underline{\boxed{\sf m=\dfrac{-v}{u}}}$

Solution :

$\implies{\sf \dfrac{1}{30}=\dfrac{1}{v}+\dfrac{1}{12}}$

$\implies{\sf \dfrac{1}{v}=\dfrac{1}{30}-\dfrac{1}{12}}$

$\implies{\sf \dfrac{1}{v}=\dfrac{12-30}{30 \times 12}}$

$\implies{\sf v =\dfrac{360}{-18}}$

$\implies{\bf v = -20\: cm}$

Characteristics of image -

• Any position of object in a Convex mirror , image is always formed between Pole and Focus

• Image is small , erect and virtual

➞ Magnification

$\implies{\sf m=\dfrac{-v}{u} }$

$\implies{\sf m = \dfrac{-(-20)}{12}}$

$\implies{\bf m = +1.6}$

Answer :

image distance from mirror (v) = -20cm

Magnification (m) = +1.6