Question

Find the position and nature of image of object of height 3 cm,when placed 60 cm from a convex mirror of focal length 15 cm. Draw a ray diagram?

Answer 1

Solution :

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

• Distance of object from mirror, (u)  = -60 cm
• Height of object, (h1) = 3 cm
• Focal length, (f) = 15 cm

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

As we know that formula of the mirror :

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

$\longrightarrow\sf{\dfrac{1}{f} = \dfrac{1}{u} + \dfrac{1}{v} }\\\\\\\longrightarrow\sf{\dfrac{1}{15} =\dfrac{1}{-60} +\dfrac{1}{v} }\\\\\\\longrightarrow\sf{\dfrac{1}{v} =\dfrac{1}{15} +\dfrac{1}{60} }\\\\\\\longrightarrow\sf{\dfrac{1}{v} = \dfrac{4+ 1}{60} }\\\\\\\longrightarrow\sf{\dfrac{1}{v} =\dfrac{5}{60} }\\\\\\\longrightarrow\sf{5v=60}\\\\\longrightarrow\sf{v=\cancel{60/5}}\\\\\longrightarrow\bf{v=12\:cm}$

∴ Image is real & Inverted, Image will be formed 12 cm .