Optics
• Objectives
– Understand how converging and diverging mirrors and lenses create images
– Utilize the simple lens equation for focal length
Converging Lens
• Light parallel to the optical axis converges to the focal point
after the converging lens. (+ lens, + focal length)
-
0
+
Diverging Lens
• Light parallel to the optical axis diverges away from the
focal point after the diverging lens. (- lens, - focal length)
-
0
+
Near-sightedness Correction
Eye too
long,
focal
length
too
short.
Far-sightedness Correction
Eyeball too short, focal length too long.
Magnification Calculation
do = object distance from the mirror or lens as measured from
the center of the lens or mirror, along the optical axis.
di = image distance from the mirror or lens as measured from
the center of the lens or mirror, along the optical axis.
ho = object size as measured from the optical axis.
hi = image size as measured from the optical axis. (+ upright)
M = - di /do = hi / ho
**sign convention: focal lengths are positive if located in
“real” space, negative if located in “virtual” space. A negative
magnification indicates an inverted image.
Image Distance Calculation
What type of image is formed by a 2 cm high object located
15 cm in front of a converging lens of focal length 8 cm?
Using our equations
1/f = 1/do + 1/di
1/8 = 1/15 + 1/di
1/di = 1/8 - 1/15
= 0.058
di = 1/0.058
= 17.1 cm
Image Magnification and Size
M = - di /d o
= - 17.1 / 15
= - 1.14
The magnification is slightly greater than 1.0 indicating a
slightly larger image than object. It is negative indicating
an inverted image compared to the upright object.
Its size is
M = h i /h o
- 1.14 = hi / 2 cm
hi = - 2.28 cm
Image Distance Calculation
What type of image is formed by a 5 cm high object located
20 cm in front of a diverging lens of focal length 10 cm?
Using our equations
1/f = 1/do + 1/di
-1/10 = 1/20 + 1/di
1/di = -1/10 - 1/20
= - 0.15
di = - 1/0.15
= - 6.6 cm
Image Magnification and Size
M = - di /d o
= - -6.6 / 20
= 0.33
The magnification is 1/3 creating a smaller image than object.
It is positive indicating an upright image compared to the
object.
Its size is
M = h i /h o
0.33 = hi / 5 cm
hi = 1.67 cm