Two lense system

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) ....

•

• 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.

• 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.

•

• A similar process will produce the image

for a double lens system involving a

converging and a diverging lens.

•

• 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.

Two-lens system - example

• 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

• 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