Question

If a man's face is 25cm in front of concave shaving mirror producing erect Image 1.5 times the of face ,what is the focal length

Answer 1

Given:

Man's face is 25 cm in front of concave shaving mirror. Erect image is being produced 1.5 times the size of the face.

To find:

Focal length of mirror.

Calculation:

Magnification of a concave mirror is given as :

$\rm{mag. = - \dfrac{v}{u} = \dfrac{h _{i}}{h_{o} } }$

$\rm{ = > - \dfrac{v}{( - 25)} = 1.5 }$

$\rm{ = > v = 1.5 \times 25 }$

$\rm{ = > v = \dfrac{75}{2} \: cm }$

Applying Mirror Formula :

$\rm{ \therefore \: \dfrac{1}{f} = \dfrac{1}{v} + \dfrac{1}{u} }$

$\rm{ = > \: \dfrac{1}{f} = \dfrac{2}{75} + \dfrac{1}{( - 25)} }$

$\rm{ = > \: \dfrac{1}{f} = \dfrac{2}{75} - \dfrac{1}{25} }$

$\rm{ = > \: \dfrac{1}{f} = \dfrac{2 - 3}{75} }$

$\rm{ = > \: \dfrac{1}{f} = \dfrac{ - 1}{75} }$

$\rm{ = > \: f = - 75 \: cm }$

So , final answer is:

Focal length of mirror is 75 cm

Answer 2

Focal length of mirror is 75 cm