Question

A converging lens (f = 10.1 cm) is located 26.3 cm to the left of a diverging lens (f = -4.93 cm). A postage stamp is placed 43.9 cm to the left of the converging lens. (a) Locate the final image of the stamp relative to the diverging lens. (b) Find the overall magnification.

Answer 1

focal length of Converging lens f0 = 10.1 cm
Distance of object from converging lens d0 = 43.9 cm
Let Distance of image from converging lens be di
Let Magnification of Converging lens be Mc

we know,
1/fo = 1/do + 1/di
1/di = 1/fo - 1/do
di = 1/ (1/10.1 - 1/43.9)
di = 13.12 cm

We Know,
M = - di / do
Mc = - 13.12 / 43.9
Mc = - 0.2988

Now, Image of converging lens is also Object of Diverging lens

Distance of object from Diverging lens = Distance between two lens - Distance of image from Converging lens
Distance of object from Diverging lens = 26.3 cm - 13.12cm
Distance of object from Diverging lens = 13.18 cm

Focal length of Diverging lens fd = -4.93 cm

1/fo = 1/do + 1/di
-1/4.93 = 1/13.18 + 1/di
1/di = -  (1/4.93 + 1/13.18 )
di = -1/(1/4.93 + 1/13.18 )
di = - 3.587 cm

Magnification due to diverging lens Md = -di / do
Magnification due to diverging lens Md = - (-3.587 / 13.18 )
Magnification due to diverging lens Md = 0.272

a)
Final Image of the stamp relative to Diverging lens di = - 3.587 cm

b)
Total Magnification M = Magnification due to diverging lens * Magnification due to Converging lens
Total Magnification M = 0.272 * - 0.2988
Total Magnification M = -0.081