Question

An object is kept 14 cm in front of a concave mirror . It forms a real image 4 times larger than the object . Find the distance of image from mirror

Answer 1

Solution :

$\underline{\bf{Given\::}}}$

• Focal length of concave mirror, (f) = -14 cm
• Magnification, (m) = 4

$\underline{\bf{Explanation\::}}}$

When image is real & Inverted, magnification will be negative.

As we know that linear magnification;

$\mapsto\sf{m=\dfrac{-v}{u} }\\\\\mapsto\sf{-4=\dfrac{-v}{u} }\\\\\mapsto\sf{\cancel{-}4u = \cancel{-} v}\\\\\mapsto\bf{v =4u}$

Now, using formula of the spherical mirror;

$\boxed{\bf{\frac{1}{f} =\frac{1}{v} +\frac{1}{u} }}}$

$\longrightarrow\sf{\dfrac{1}{-14} = \dfrac{1}{4u} + \dfrac{1}{u} }\\\\\\\longrightarrow\sf{\dfrac{1}{-14} = \dfrac{1}{4u} + \dfrac{1}{u}}\\\\\\\longrightarrow\sf{\dfrac{1}{-14} = \dfrac{1+4}{4u} }\\\\\\\longrightarrow\sf{\dfrac{1}{-14} = \dfrac{5}{4u} }\\\\\longrightarrow\sf{4u = -70}\\\\\longrightarrow\sf{u=-\cancel{70/4}}\\\\\longrightarrow\bf{u=-17.5\:cm}$

Hence, u = -17.5 cm

So, object will be placed at a distance of 17.5 cm in front of the mirror .

Answer 2

Answer:

Ok

Explanation:

Ok