Answer to Question #192446 in Optics for Harry

Question

Two lenses, one converging with focal length 20.0 cm and one diverging with focal length are placed 25.0 cm apart. An object is placed 60.0 cm in front of the converging lens. Determine (a) the position and (b) the magnification of the final image formed. (c) Sketch a ray diagram for this system.

Answer 1

(i) For converging lens

$f=20cm, u=-60cm$

using lens formula-

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

$\Rightarrow \dfrac{1}{v}=\dfrac{1}{f}+\dfrac{1}{u}$

            $=\dfrac{1}{20}-\dfrac{1}{60}=\dfrac{2}{60}=\dfrac{1}{30}$

Taking reciprocal we get-

$v=30 cm$

This distance will behave as an object for diverging lens.

For diverging lens-

$u=5cm,$ ( since distance between images is 25cm)

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

      $=\dfrac{-1}{10}+\dfrac{1}{5}=0.1$

Taking reciprocal

$v=10cm$

(b) Magnification of converging lens $(m_1)=\dfrac{v}{u}=\dfrac{30}{-60}=-0.5$

  Magnification of diverging lens $(m_2)=\dfrac{v}{u}=\dfrac{10}{5}=2$

Total Magnification $M=m_1m_2=-0.5\times 2=-1$

(c) Ray diagram is-