# An upright object is placed at a distance of 40 cm in front of a convergent lens of focal length 20 cm. A convergent mirror of focal length 10 cm is placed at a distance of 60 cm on the other side of the lens. The position and size of the final image will be : Option 1) $20\; cm$ from the convergent mirror, same size as the object   Option 2) $20\; cm$ from the convergent mirror, twice the size of the object Option 3) $40\; cm$ from the convergent mirror, same size as the object   Option 4) $40\; cm$ from the convergent lens, same size of the object

$\rightarrow Total \; 3 \; process$

(1) Refraction from lense

$u =-40\; cm,\; \; f=+20\; cm$

$\Rightarrow V=+40\; cm, (Image\; I_{1})$

and $m_{1}=-1$

(2) Reflection from mirror

$u =-20\; cm,\; \; f=-10\; cm$

$\Rightarrow V=-20\; cm, (Image\; I_{2})$

and  $m_{2}=-1$

(3) Refraction from lens

$u =-40\; cm,\; \; f=+20\; cm$

$\Rightarrow V=+40\; cm, (Image\; I_{3})$

and $m_{3}=-1$

$m=m_{1}.m_{2}.m_{3}=-1$

Final image is at $40\; cm$ from convergent lens and it has same size as object.

Option 1)

$20\; cm$ from the convergent mirror, same size as the object

Option 2)

$20\; cm$ from the convergent mirror, twice the size of the object

Option 3)

$40\; cm$ from the convergent mirror, same size as the object

Option 4)

$40\; cm$ from the convergent lens, same size of the object

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