A converging lens of focal length 15cm and a converging mirror of focal length 10cm are placed 50cm apart with common principal axis. A point source is placed in between the lens and the mirror at a distance of 40cm from the lens. Find the locations of the two images formed.
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The object is placed in the focus of the converging mirror.
There will be two images.
- One due to direct transmission of light through lens.
- One due to reflection and then transmission of the rays through lens.
u = -40cm, f = 15cm
$\Rightarrow\frac{1}{\text{v}}-\frac{1}{\text{u}}=\frac{1}{\text{f}}\Rightarrow\frac{1}{\text{v}}=\frac{1}{15}+\frac{1}{-40}$
$\Rightarrow\text{v}=24\text{cm}$ (left of lens)
Case II: (S'') Since, the object is placed on the focus of mirror, after reflection the rays become parallel for the lens.
So, $\text{u}=\infty$
$\Rightarrow\text{f}=15\text{cm}$
$\Rightarrow\frac{1}{\text{v}}-\frac{1}{\text{u}}=\frac{1}{\text{f}}\Rightarrow \text{v}=15\text{cm}$ (left of lens).
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