1. . y y’ A B a a’ = C D OPTICAL SYSTEM GEOMETRICAL OPTICS
Paraxial approximation: LINEAR OPERATIONS ON RAYS y
OPTICAL
SYSTEM a’ y’ a y’ a’ = .
A B
C D y a

2. 1 L 1 0 0 1 1 0 1 0 1 n2 n1 n1 n2 n2 n1 n1 n2 n1 - Rn2 PROPAGATION
STRAIGHT INTERFACE
1 L
0 1
1 0 n2 n1 n1 n2 n2 n1
POSITIVE LENS
CURVED INTERFACE n1 n2
n1 -
Rn2
1 0 1 - f R

3. IMPORTANT EXAMPLES
Glass plate
Thick lens
Find the focal distance
Find the magnification, transverse and longitudinal
Find the image location – real of virtual
The “equivalent” thin lens

4. F

5. f
1.5 1 1 2 3

6. f Si = -3/5 1 si 1 1 1.5 ai = a 2/5 0 1 5/2 = 1.5+2.5si 2.5 a 1+si si
Neg
lens
Neg
lens f
Concave
mirror
Si = -3/5
Angular magnification 2.5 1 si 1 1
1.5 ai = a
Matrix to image: 2/ /2 = si
2.5 a
1+si si 1
1.5 1 a
Magnification: 2/ /2 y =
2y/5

7. 2/5 0 1 5/2 y’ = (2/5) x y a’= y + (5/2) x a Significance of
Matrix to image: 2/ /2
Significance of
y’ = (2/5) x y
a’= y + (5/2) x a
Inclination from the ray coming from the lens

8. f new s0 = 18/5 Si = -3/5 1 si 1 1 1.5 ai = a 2/5 0 1 5/2 = 1.5+2.5si
Neg
lens
Neg
lens f
Concave
mirror
new s0 = 18/5
Si = -3/5
Angular magnification 2.5 1 si 1 1
1.5 ai = a
Matrix to image: 2/ /2 = si
2.5 a
1+si si 1
1.5 1 a
Magnification: 2/ /2 y =
2y/5

9. f Si = 18/13 Si = -3/5 S0 = 18/5 1 -1 si a 1 18/5 ai = -5/13 0
Neg
lens
Neg
lens f
Concave
mirror
Si = 18/13
Si = -3/5
S0 = 18/5 1 -1 si a 1
18/5 ai =
Angular magnification -13/5
Matrix to image:
-5/ /5 =
18/5-13/5si
-13/5 a
1-si si -1 1
18/5 1 a
-5/ /5 y =
-5y/13 -y
Magnification:

10. f Si = 18/13 Si = -21/34 S0 = 21/13 a 1 21/13 si ai = 13/34 0 1 34/13
Neg
lens
Neg
lens f
Concave
mirror
Si = 18/13
Si = -21/34
S0 = 21/13 a 1
21/13 si ai =
Angular magnification 34/13
Matrix to image:
13/
/13
21/13 1 a
1+si si =
21/13+34/13si
34/13
Magnification:
13/
/13 y =
13y/34 -y

11. TOTAL FROM OBJECT TO FINAL IMAGE
Neg
lens
Neg
lens f
Concave
mirror
Matrix from object to image:
13/
/13
-5/ /5 2/ /2
Magnification:
13/34 x (-5/13) x 2/5

12. Find the longitudinal and transverse magnification of the meter stick,
with a negative and positive lens.

13. f = 40 cm 160 cm 60 cm Meter stick Si = 120 a 1 60 1/40 si ai = a 1
Meter stick – longitudinal image by a
Positive lens
f = 40 cm
160 cm
60 cm
Meter stick
Hint: in this particular case, make your life easier by choosing as unit f
60-si/2
-1/2
Si = 120 a 1 60
1/40 si ai =
160-3si -3 a 1
160
-1/40 si ai =
Si = 53.33

14. f = -40 cm 160 cm 60 cm Meter stick Si = -24 a 1 60 1/40 si ai = a 1
Meter stick, image by a negative lens
(3-9)
f = -40 cm
160 cm
60 cm
Meter stick A B
Hint: in this particular case, make your life easier by choosing as unit f
60+5si/2
-1/2
Si = -24 a 1 60
1/40 si ai =
160-5si -3 a 1
160
1/40 si ai =
Si = -32