Question

Find the final position of the image of the object O from the mirror $m_1$ after three successive reflections taking first reflection on $m_1$.

• A. $10.5\text{cm}$
• B. $12.5\text{cm}$
• C. $25\text{cm}$
• D. $-30\text{cm}$

Answer 1

The correct option is B $12.5\text{cm}$


For $1^{st}$ reflection:

$u=-15\text{cm};f=-10\text{cm}(\because f=\frac{R}{2})$

Using mirror formula

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

$\Rightarrow \frac{1}{v}=\frac{-1}{10}+\frac{1}{15}=\frac{-3+2}{30}$

$\Rightarrow v=-30\text{cm}$

$\therefore$ First image$I_1$ from $M_2=10cm$

After $2^{nd}$ reflection, second $I_2$ image will be formed on right side of $M_2$.

For $3^{rd}$ reflection from $m_1$:

$u=-(40+10)=-50\text{cm};f=-10\text{cm}$

Again using mirror formula

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

$\Rightarrow \frac{1}{v}=\frac{1}{f}-\frac{1}{4}=\frac{-1}{10}+\frac{1}{50}$

$\Rightarrow v=\frac{-50}{4}=-12.5\text{cm}$

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