Alternative derivation of the thin lenses formula. Considering surface-1.
Considering surface-2. (For the case shown in the figure, R1 is a positive number
).
Thin lenses
C2
C1
Optical axis
Alternative derivation of the thin lenses formula
R1
R2
SS0o
C2
no
nl (1)
ni
C1
Si1
Si2
(2)
S0
Si1
Considering surface-1 (For the case shown in the figure, R1 is a positive number)
Considering surface-2
(For the case shown in the figure, R2 is a negative number) Adding up the last two expressions
= which is the same expression obtained in the previous section
Summary
surface-1
no
no
nl
surface-2
Example
Example
1
2
Both R1 and R2 are negative numbers
=
= =
Example
Optical center
C2
C1
Ray tracing with thin lenses
The eye
Newtonian form of the lens equation
Thin lens combinations Fo1
Fi1
Fo1
Fi1
Fig-1
Fi1 Fi2 F01
Fig-2.
So we need to determine just one more ray.
Notice also that, now that point B' has been determined, we can draw any arbitrary ray from B to B' that passes through the lens-1 ( see ray BPB' in the figure). Option-1 We will see below (step-4), that is is convenient to select a ray BPB' such that, when PB' is traced backwards it crosses the optical axis at the point Fo2 (see Fig.3).
Fi1 F01
P
Fi2 (ii)
F02 Fig-3
Option-2 Alternatively, it will be also convenient to draw a ray from B that passes through the focal point F01.
Fig-4 Do not do this.
Fi2 F02
Option-1 Page 51
. See also Fig-3 above.
Since B' has already been determined, we can always draw the line F02 B'.
(But keep in mind that lens 1 has to be placed between F02 and lens-2. See also Fig-3 above).
