- When using a two lens optical system, the magnification of the final image is calculated by multiplying the magnifications of each individual lens. - To calculate the image from the first lens, treat it as the object for the second lens. The object distance for the second lens is the distance from the first lens' image to the second lens. - A two converging lens system will produce a real, upright final image, while a converging-diverging system will produce a virtual, inverted final image.

1. Two lense system

2. Two lense system:
• When two or more lenses are used in an optical
system, the formula used to calculate the
magnification of the final image produced by the
system is:
•
Msystem = (Mlens #1)(Mlens #2)(Mlens #3) ....
•

3. • When an optical system uses two lens, work
each lens separately. Remember that the image
of lens #1 will serve as the object for lens #2. If
the image of lens #1 falls "in front of" lens #2,
you can calculate the object distance for lens #2
by subtracting the value of di for lens #1 from the
total distance separating the two lenses.

5. • In this example, two converging lens produce a
final image which is real and upright. A scaled
diagram would be necessary to determine how
the height of the final image, I2, compares to the
height of the original object, O.
•

6. • A similar process will produce the image
for a double lens system involving a
converging and a diverging lens.

7. •

8. • In this second example, a converging lens
followed by a diverging lens produce a final
image which is virtual and inverted. A scaled
diagram would be necessary to determine how
the height of the final image, I2, compares to the
height of the original object, O.

9. Two-lens system - example

10. • In most cases, though, it is easier to work
through the analysis of the system from first
principles. Consider an objective lens of focal
length 100 mm, eyepiece of focal length 75 mm,
450 mm apart. Then if the object is 150 mm to
the left of lens 1 the image in lens 1 will be given
by
• 1/v1 = 1/f1 + 1/u1 = 1/100 – 1/150 = 300

11. • that is 300 mm to the right of lens 1, or 150 mm
to the left of lens 2. Thus the final image will be
given by
• 1/v2 = 1/f2 + 1/u2 = 1/75 – 1/150 = 1/150
The overall magnification is given by
M = v1/u1 v2/u2 = 300/-150 150/-150 = 2