Question

An object 4cm high is placed at a distance of 15cm in front of a concave mirror of focal length 12cm. Find the positionof the image formed. Also based on the position and nature of the image formed, mention anapplication of the concave mirror.

Answer 1

Explanation:

Given :-

• object height,h = 4 cm
• object distance, u = -15 cm
• focal length, f = -12 cm

To find :-

• image distance,v
• magnification

Using mirror formula,

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

$\frac{1}{ - 12} = \frac{1}{v} + \frac{1}{( - 15)}$

$\frac{1}{ - 12} = \frac{1}{v} - \frac{1}{ 15}$

$- \frac{1}{12} + \frac{1}{15}$

$\frac{5 - 4}{60} = \frac{1}{v}$

$\frac{1}{v} = \frac{1}{60}$

$\boxed{v = 60 \: cm}$

We know that,

$Linear \: magnification = \frac{ {h}^{i} }{h} = - \frac{v}{u}$

$\frac{ {h}^{i} }{4} = \frac{ - 60}{ - 15}$

$\frac{ {h}^{i} }{4} = 2$

$\boxed{ {h}^{i} = 8 \: cm}$

Application of concave mirror,

• It is used for shaving mirrors.
• It is used by dentist.
• It is used in solar cooking.