Transcript Thin Lens Equation

Thin Lens Equation
• Distances of virtual images are negative & distances of real
images are positive.
• Heights are positive if upright (above P.A.) and negative
(below P.A.)
• Converging lens has a real focal point (F) and a positive
focal length (f)
• Diverging lens has a virtual focal point (F) and a negative
focal length (f)
To remember which side of the lens the focal point should
be, try to imagine where the focal point would be if the
parallel rays of light passed through the lens.
Magnification Equation
• An upright image (above the P.A.) has a
positive magnification.
• An inverted image (below the P.A.) has a
negative magnification.
Practice Problem 1
An object 8.5 cm high is placed 28 cm from a converging
lens. The focal length of the lens is 12 cm. Hint: is f + or −?
a) Calculate the image distance
b) Calculate the image height
a)
Givens:
f = 12 cm
ho = 8.5 cm
do = 28 cm
Required:
a) di = ?
b) hi = ?
1 1 1
 
f di do
1 1 1
 
di f do
1 1 1
 
di 12 28
1
7
3


di 84 84
1
4

di 84
4di  84
di  21cm
The image is 21 cm
from the lens and is a
real image.
b)
hi  di

ho
do
hi  ( 21)

8 .5
28
28hi  178.5
hi  6.4cm
The height of the
image is -6.4 cm. The
image is inverted.
Lens Application: The Telescope
• For a very distant object, the
incident rays that approach the
objective lens of the telescope
are *almost* parallel.
• An intermediary real image is
formed using an objective lens.
This image then becomes the
object for the next lens
(ocular).
• The light rays from
intermediary image spread out
until it reaches the eyepiece
and enters the eye of observer.
• Observer traces the rays to
form a virtual inverted image of
the original object.
Lens Application: The Eye
• Light enter the eye through the clear cornea which refracts it.
• The pupil is a hole that allows light to pass through. The size of
the pupil is controlled by the iris (coloured part of eye)
muscles.
• Eye has a converging lens that collects the light and refracts it
to a focal point. Using its muscles, the lens can change the
focal length to increase its focal power for very close objects.
Image is formed on the
retina (the screen) and is
real & inverted. The
optic nerve sends this
information to the brain
which then interprets it
as right side up!
Correcting Vision: Myopia
• Nearsightedness
• Can see objects up close but
have difficulty with distant
objects
• Eyeball is too long relative to
the focusing power of
cornea/lens of eye.
• Light ray focuses at a point
before the retina rather than
directly on the retina.
• Use diverging lens so light rays
can diverge more to reach the
surface of retina in order for
image to be formed.
Correcting Vision: Hyperopia
• Farsightedness
• Can see distant objects but
have difficulty with objects up
close
• Eyeball is too short relative to
the focusing power of
cornea/lens of eye.
• Light ray focuses at a point
beyond the retina rather than
directly on the retina.
• Use converging lens so light
rays can converge earlier to
reach the surface of retina in
order for image to be formed.
Correcting Vision: Astigmatism
• Cornea and/or lens is not
shaped correctly.
• Image cannot be focused
correctly and projected
on the retina (or it is
formed on more than one
place on the retina).
• Corrected using
eyeglasses, contact (toric)
lenses or laser eye
surgery.