Question

Find the position of final image after three successive reflections taking first reflection on $m_1$

• A. $-12.5cm$
• B. 12.5 $cm$
• C. 30 $cm$
• D. $-30cm$

Answer 1

The correct option is A $-12.5cm$

Given,

For $1st$ reflection:

The focal length is $f=-10cm$

The object distance is $u=-15cm$

Applying the mirror formula to get the image distance,

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

$\frac{1}{v}=\frac{1}{-10}-\frac{1}{-15}$

$v=-30cm$

For $2nd$reflection:

The focal length is $f=10cm$

The object distance is $u=-10cm$

Applying the mirror formula to get the image distance,

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

$\frac{1}{v}=\frac{1}{10}-\frac{1}{-10}$

$v=10cm$

For $3rd$ reflection:

The focal length is $f=-10cm$

The object distance is $u=-50cm$

Applying the mirror formula to get the image distance,

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

$\frac{1}{v}=\frac{1}{-10}-\frac{1}{-50}$

$v=-12.5cm$ .