Question

A convex mirror whose focal length is 10cm forms an image of an object placed at distance of 15cm from the mirror. Determine the position of the image formed.

Answer 1

Given : –

• Focal length of the convex mirror [ f ] = +10 cm .
• Distance of the object [ u ] = -15 cm .

To Find : –

• Position of the image formed [ v ] = ?

Solution :–

By using mirror formula –

$\bf{ \dfrac{1}{f} = \dfrac{1}{v} + \dfrac{1}{u} }$

→ $\sf{ \dfrac{1}{10} = \dfrac{1}{v} + \dfrac{1}{ - 15} }$

→ $\sf{ \dfrac{1}{10} = \dfrac{1}{v} - \dfrac{1}{ 15} }$

→ $\sf{ \dfrac{1}{v} = \dfrac{1}{10} + \dfrac{1}{15} }$

→ $\sf{ \dfrac{1}{v} = \dfrac{3 + 2}{30} }$

→ $\sf{ \dfrac{1}{v} = \dfrac{ \cancel{\:5}}{ \cancel{30}} }$

→ $\sf{ \dfrac{1}{v} = \dfrac{1}{6} }$

→ $\underline{\fbox{ \sf{v = 6}}}$

So, the position of the image formed is 6 cm .

• Image will be virtual and erect .
• Image will formed behind the mirror .
• Size will be diminished .