Question

When an object size is 7cm is placed at a distance of 27cm in front of the concave mirror of focal length 18cm . Find the image distance

Answer 1

Answer:

$\bigstar$ Given:

⇒ Object height ($h$) = $7\, cm$

⇒ Object distance ($u$) = $-27 \, cm$

⇒ Focal length of the concave mirror ($f$) = $- 18 \,cm$

$\bigstar$ To Find:

⇒ Image distance

$\bigstar$ Solution:

Using the Mirror Formula,

$\purple{\large{\boxed{\dfrac{1}{f} =\dfrac{1}{v} + \dfrac{1}{u} }}}$

$\dfrac{1}{v} =\dfrac{1}{f} - \dfrac{1}{u} }}$

$\dfrac{1}{v} =\dfrac{1}{-18} - \dfrac{1}{-27} }}$

$\dfrac{1}{v} =\dfrac{1}{-18} + \dfrac{1}{27} }}$

$\dfrac{1}{v} =\dfrac{-3 + 2}{54}$

$\dfrac{1}{v} =\dfrac{-1}{54}$

$\red{\boxed{{v = -54}}}$

Image distance (v) = $-54\,cm$

$v$ is (– ve) screen should be placed at 54cm in front of the mirror.

Hence, image is formed on the same side.

To find the height; we use the formula,

$\large{\boxed{m=\dfrac{h\,'}{h} = \dfrac{-v}{u}}}$

$m = \dfrac{h\,'}{7} = \dfrac{54}{-27}$

$h' = 7 * (-2)$

$\green{\boxed{h' = -14\,cm}}$

Nature of the image :

$\mathsf{Real}\\\mathsf{Inverted}\\ \mathsf{Magnified, image\; will \;be\; of \;size \;14 cm.}$