Post on 17-Dec-2015
Geometric Optics
Reflection, Refraction and
Lenses
Refraction in LensesOBJECTIVES
Understand how light is refracted and transmitted through lenses to form images.
Know the difference between concave and convex lenses?
Master the skill of constructing ray diagrams of objects in front of lenses to predict where an image will be and what it will look like.
Lenses
• Convex• Concav
e
Lens is a piece of transparent material, such as glass or plastic, that is used to focus light and form an image.
Convex Lenses• Convex lens is thicker at the center than at the edges
• Convergent lenses because they refractparallel light rays so that the rays meet at a point – focal point.
• Rays from distant objects are parallel So focal point can be found by locating point where the suns rays are brought to a sharp image
F
• Lenses are thinner in the middle than around the edges.
• Divergent lenses because when surrounded by material with a lower index of refraction, rays passing through it spread out.
• The focal point is the point from which the diverging rays seem to emerge
Concave Lenses
F
Convex Lens
Principalaxis
C Fxx
Ax
fR
C: Center of curvatureR: Radius of curvature (2f)F: Focal Pointf: focal lengthA: vertex, center of lens
Optical axis
Fx
R
xC
f
Lens
C Fxx
Ax
The image location of an object in front of a lens is the location where all its light intersects after refracting and passing through the lens. The image is the intersection point of all refracted rays.
Fx x
C
Object
Ray tracingTo find the image of an object, we will trace a few rays through the lens and see where they intersect. The intersection of rays after passing through the lens locates the image of the object
Ray tracing is a method of constructing an image using the model of light as a ray.
We use ray tracing to construct optical images produced by mirrors and lenses
Ray tracing lets us describe what happens to the light as it interacts with a medium
C
Fxx
Ax
Fx x
C
Object
Ray Diagram-Convex lens
Principal ray
Focal ray
Central ray
Image of top
of object
Image
This Image isLocated opposite
side, beyond C
Real Inverted and Enlarged in size
Ray tracingTo find the image of an object, use the following principal rays
• the p-ray, which travels parallel to the principal axis, then refracts through the focal point.
• The f-ray, which travels through the focal point, then refracts parallel to the principal axis.
• The c-ray, which travels through the center of the lens and continues without bending.
Ray Diagram-Concave lens
Object f f
Principal ray
Focal ray
Central ray
Image
This Image isLocated same side,
inside fVirtual (on same
side) Upright and Reduced in size
Optical Image Location Orientation
• upright• inverted
Size• True• Enlarged• Reduced
Type• real (converging rays)• virtual (diverging rays)
OBJECT Location CONVEX Lens IMAGE
Location Orientation Size Type
Beyond C Between C and FOther side inverted Reduced real
At C At C Other Side Inverted True real
Between C and F
Beyond COther side Inverted Enlarged real
At F NO IMAGEInside F Same Side Upright Enlarged Virtual
OBJECT Location CONCAVE Lens IMAGE
Location Orientation
Size Type
Very far away Inside FSame Side Upright Reduced Virtual
Very close Inside FSame Side Upright Reduced Virtual
The Lens Equationdo di
Object ff Image
hi
ho
f
fd
h
h i
o
i
o
i
o
i
d
d
h
h
Thin Lens EquationThe thin lens equation relates the focal length of a spherical thin lens to the object position and the image position
di is positive for real images
di is negative for virtual images
f is positive for convex, converging lensesf is negative for concave, diverging lenses
Lateral Magnification
o
i
o
i
d
d
h
hm
hi is positive for upright images
hi is negative for inverted images
Example: Image formed by converging lens. What is a) the position and b) the size of the image of a large 7.6 cm high flower placed 1.00 m from a 50.0 mm focal length camera lens?
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a) Image is behind lens, only 2.6 mm farther from the lens than would be the image for an object at infinity.
Example: Image formed by converging lens. What is a) the position and b) the size of the image of a large 7.6 cm high flower placed 1.00 m from a 50.0 mm focal length camera lens?
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d
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oi
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b)
Image is 4 mm high and inverted (m<0)
Example: Object close to a converging lens. An object is placed 10 cm from a 15 cm focal length converging lens. Determine the image position and size (a) analytically and (b) using a ray diagram
f f
a)
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30
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1
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15
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since di<0, image is virtual and on same side of the lens.Since m>0, image is upright
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i
d
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Example: Object close to a converging lens. An object is placed 10 cm from a 15 cm focal length converging lens. Determine the image position and size (a) analytically and (b) using a ray diagram
f f
b)
Image is virtual and upright
Example: Diverging lens. Where must a small insect be placed if a 25 cm diverging lens is to form a virtual image 20 cm in front of the lens?
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f
DO NOW
An object is located 139.0 mm from a 50 mm focal length converging lens. Find the image distance and magnification a) by using a ray diagram b) by calculation
f f
a)
Image is real, inverted and reduced
6.02.1
75.0
units
units
h
hm
o
i
DO NOW
An object is located 139.0 mm from a 50 mm focal length converging lens. Find the image distance and magnification a) by using a ray diagram b) by calculation
f fb)
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11
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56.0139
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Image is real, inverted and reduced
http://www.phys.ufl.edu/~phy3054/light/lens/applets/Welcome.html
http://www.physics.uoguelph.ca/applets/Intro_physics/kisalev/index.html
Lenses
DO NOWAn object 31.5 cm in front of a certain lens is imaged 8.20 cm in front of that lens (on the same side as the object). What type of lens is this and what is its focal length? Is the image real or virtual? Confirm with ray diagram.
f f
a)
Lens is divergingcmf
ddf io
11
2.8
1
5.31
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Chromatic Aberration • Light that passes through a lens is ringed with
color – This results from dispersion of light by the lens– Always present when a single lens is used– Can be corrected by using two lenses
Our Eyes & LensesLight that is emitted or
reflected off an object travels into the eye through the cornea.
The light then passes through the lens and focuses onto the retina that is at the back of the eye.
Specialized cells on the retina absorb this light and send information about the image along the optic nerve to the brain.
Focusing Images
Light entering the eye is mostly focused by the cornea because the air-cornea surface has the greatest difference in indices of refraction (cornea n=1.376).
The lens is responsible for the fine focus that allows you to clearly see both distant and nearby objects.
Accommodation • Muscles surrounding the lens can
contract or relax, thereby changing the shape of the lens.
This, in turn, changes the focal length of the eye. When the muscles are relaxed, the image of distant objects is focused on the retina.
When the muscles contract, the focal length is shortened, and this allows images of closer objects to be focused on the retina.
Distant vision
Close vision
Nearsightedness
– Focal length of the eye is too short to focus light on the retina.
– Also known as myopia
– Objects far away are blurry
– Fixed with concave lenses
Farsightedness–Focal length of the
eye is too long and places image past the retina
–Also known as hyperopia
–Objects nearby are blurry
–Fixed with convex lenses
Camera
Example: An 80 mm focal length lens is used to focus an image on the film/sensor of a camera. The maximum distance allowed between the lens and the sensor plane is 120mm.A) how far ahead of the film should the lens be if the object to be photographed is 3.0 m away??B) What is the closest object this lens could photograph?
f f
a)
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Example: An 80 mm focal length lens is used to focus an image on the film/sensor of a camera. Maximum distance allowed between the lens and the sensor plane is 120mm.B) What is the closest object this lens could photograph?
f f
b)
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1
80
11
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Refracting Telescope– Lenses magnify distant objects– Light from stars and galaxies so far
away that light is parallel and makes a real image
Objective lens Eyepiece
Binoculars– Lenses produce magnified images of faraway
objects• Just as separation of your eyes gives a sense of 3D
and depth, the prisms allow greater separations of the objectives, thereby improving 3-D
Microscope– Used to view very small objects