Question

an object moving at a speed of 5m is towards a concave mirror of focal length f =14 is at a distance of 9m. the average speed of the image is

Answer 1

Given :

Speed of the image = 5m/s

Focal length of the concave mirror = 1m

Object distance = 9m

To find :

The average speed of the image

Solution :

• We know that for a concave mirror,   $\frac{1}{f} =\frac{1}{u} +\frac{1}{v}$

• By substituting the values

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

       $\frac{1}{-1} =\frac{1}{-9} -\frac{1}{v}$

        $\frac{1}{v} =\frac{-10}{9}$

       $v =\frac{-9}{10}$

• Let's consider the time period as one second

• Object distance = 9-5 =4m

• The new image distance can be obtained by the formula

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

       $\frac{1}{-1} =\frac{1}{-4} -\frac{1}{v}$

        $v =\frac{-4}{5}$

• The change in image distance  $=\frac{-9}{10} -\frac{-4}{5}$

                                                             $=\frac{1}{10} m$

• Average speed of object  $=\frac{Distance\:travelled}{Time\:taken}$

                                                    $=\frac{1}{10}m/s$

The average speed travelled by the particle is 1/10 m/s