Question

4. An object is placed at 20 cm in front of a convex mirror of focal length 10 cm. calculate the position of the image. ​

Answer 1

Solution:-

$\rm \to \: object \: distance(u) = 20 \: cm$

$\rm \to \: focal \: length \: = 10 \: cm$

To find

$\rm \to \: position \: of \: the \: image$

Formula

$\rm \to \boxed{ \rm\dfrac{1}{f} = \dfrac{1}{v} + \dfrac{1}{u} }$

Using sign convention

=> object distance is opposite to the Incident ray so

u = - 20cm

=> Focal length is always +ve in convex mirror

Now put the value on formula

$\rm \to \dfrac{1}{10} = \dfrac{1}{v} - \dfrac{1}{20}$

$\rm \to \: \dfrac{1}{10} + \dfrac{1}{20} = \dfrac{1}{v}$

$\rm \: \to \: \dfrac{1}{v} = \dfrac{2 + 1}{20}$

$\rm \to \: \dfrac{1}{v} = \dfrac{3}{20}$

$\rm \to \: v = \dfrac{20}{3}$

$\rm \: v = 6.67 \: cm \:$

=>Image is form behind the mirror

=> Nature of image is virtual and erect