Download GEOMETRIC OPTICS I. What is GEOMTERIC OPTICS In geometric

GEOMETRIC OPTICS
I. What is GEOMTERIC OPTICS
In geometric optics, LIGHT is treated as imaginary rays. How these rays interact with
at the interface of different media, including lenses and mirrors, is analyzed.
LENSES refract light, so we need to know how light bends when entering and
exiting a lens and how that interaction forms an image.
MIRRORS reflect light, so we need to know how light bounces off of surfaces
and how that interaction forms an image.
II. Refraction
We already learned that waves passing from one media to another cause
light to do two things:
Change path
Change wavelength which means…Change velocity (speed of light)
The velocity DECREASES and the wavelength SHORTENS when light passes
from a “faster” to a “slower” media.
The velocity INCREASES and the wavelength LENGTHENS when light passes
from a “slower” to a “faster” media.
In either case, the FREQUENCY remains the same.
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refraction, continued
When light hits the interface of two
media at an angle, the lower part
of the ray interacts first, thus slowing
it down before the rest of the ray
meets the interface. This rotates
the ray toward the normal.
The NORMAL LINE is an imaginary line PERPENDICULAR to the interface
of two media.
The REFRACTIVE INDEX of a substance tells you how much light will change
speed (or bend) when it passes through the substance. It is the ratio of the
speed of light in the medium to the speed of light in a vacuum.
The medium will commonly
be air, water, glass, plastic
n is the refractive index
c is the speed of light in a
vacuum
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refraction, continued
substance
vacuum
air
water
glass
refractive index, n
1
1.000277
1.333
1.50
The table of refractive index values shows you that light slows down only
a little in air, but its speed is reduced about 33% in glass.
The higher the refractive index, the slower the speed of light.
If light passes from a medium with low refractive index (air) to one of high
refractive index (glass), light refracts significantly.
SNELL’S LAW TELLS US HOW MUCH IT REFRACTS.
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refraction, continued
SNELL’S LAW: Relates the ratio of the sines of the angle of incidence and
angle of refraction of a light ray to the ratio of refractive indices of the substances
the light passes.
the 1 and 2 subscript are the
media the light ray passes.
For example, substances 1 and 2
might be air and water.
Notice how the angle of incidence and refraction are
defined with respect to the NORMAL
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III. OPTICS DEFINITIONS (LENSES AND MIRRORS)
focal point-the point on the axis of a lens or mirror to which parallel rays of light converge
or from which they appear to diverge after refraction or reflection
radius of curvature-a point beyond the focal point that indicates how curved a lens or mirror is
virtual image-an optical image from which light rays appear to diverge, although they
actually do not pass through the image
real image-An optical image such that all the light from a point on an object that passes
through an optical system actually passes close to or through a point on the image.
upright image-an optical image that is in the same orientation as the object from which the
image comes
inverted image- an optical image that is upside-down with respect to the object from which
the image comes
magnification-A measure of the effectiveness of an optical system in enlarging or reducing
an image.
dispersion-separation of light of several frequencies, such as white light, into its component.
In other words, dispersion is the name given to the separation of white light into its
colors (ROYGBIV)
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IV. PRISMS
Prisms are used to separate light into its component wavelengths. Prisms demonstrate
the optical phenomenon of DISPERSION.
Prisms are used in a number of REAL LIFE optical applications where light needs to be
selectively refracted or reflected.
violet
short λ
red
long λ
REFRACTION DEPENDS ON LIGHT WAVELENGTH OR FREQUENCY
The shorter the wavelength (higher the frequency), the more the light is refracted.
Hence, blue light is bent at a greater angle than red light.
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prisms, continued
incident
light
The ANGLE OF MINIMUM DEVIATION, δ, is
a parameter used to characterize prisms. The refractive
index of the prism is then related to the apex angle, σ of
the prism and δ as in the equation above.
δ can be found by adjusting the angle of the incident light so that
the light passes through the prism parallel to the base of the prism.
This may seem complicated but it is easy to show in the lab with a laser pointer
and a prism (and a sheet of paper that you can draw angles and stuff on).
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V. LENSES
A. CONVERGING
Converging (convex) lenses have one or both faces that bulge OUT.
It is thicker in the center than at the edges.
CONVERGING lenses FOCUS light rays PARALLEL to the horizontal axis through
the lens FOCAL POINT on the other side of the lens.
horizontal axis or
principle axis
C
C
F is the lens FOCAL POINT
C = 2F. C is the lens RADIUS OF CURVATURE
rays that are parallel to the axis are
refracted by the lens into F
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B.  How is an image produced through a converging lens
IF THE OBJECT IS OUTSIDE THE FOCAL POINT, THE IMAGE WILL BE REAL AND INVERTED.
IF THE OBJECT IS INSIDE THE FOCAL POINT. THE IMAGE WILL BE VIRTUAL AND UPRIGHT
object
REAL IMAGE
INVERTED
eye is over here
This is how a ray diagram is drawn for a converging lens. It really only takes two rays to tell where the image
will be. Two will cross where the image is located. Third ray makes sure you don’t make a mistake!
The principal ray connects the object with the lens and is then refracted THROUGH the FOCAL POINT
The central ray goes STRAIGHT THROUGH the CENTER of the lens to the image without refracting. There
is NO refraction at the center of the lens
The focal ray passes through the FOCAL POINT on the object side of the lens. It is refracted such that the
ray becomes PARALLEL to the horizontal axis. It crosses the other two rays at the image.
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C. DIVERGING LENSES
Diverging lenses have one or both faces CONCAVE. IT “cups” in and is thinner at the center.
Light rays that strike a diverging lens parallel to the horizontal axis are refracted
by the lens AWAY from the horizontal axis. Rays extended BACKWARD from the
refracted rays will intersect at the FOCAL POINT of the lens.
refracted rays extend
through the focal
point
rays parallel to
the axis
refracted away from
the axis
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D. How is an image produced through a diverging lens
IMAGES WILL ALWAYS BE VIRTUAL, UPRIGHT, AND REDUCED.
object
eye is over here
VIRTUAL IMAGE
UPRIGHT
This is how a ray diagram is drawn for a diverging lens.
The principal ray (1) connects the object with the lens and is then refracted AWAY from the FOCAL POINT.
A ray can be extended backward from the refracted ray THROUGH the FOCAL POINT on the same side as
the object.
The central ray (3) goes STRAIGHT THROUGH the CENTER of the lens and the image on the same side as
the object. There is NO refraction at the center of the lens
The focal ray (2) is refracted PARALLEL to the axis but a forward extension of the ray passes through the
FOCAL POINT on the eye side of the lens. A backward extension of the refracted ray is parallel to the axis
and goes through the image on the object side of the lens. It crosses the other two extended rays at the
image.
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E. THE LENS EQUATION
Ray diagrams are nice for analyzing the geometry of how light interacts with lenses,
but it would be a hassle to draw a scaled ray diagram to determine the distance
and magnification of an object viewed through a lens.
There are equations for that!
Locating the distance of the object, image, or focal point:
do is the distance of the
object from the lens
di is the distance of the image
from the lens
f is the focal length
Magnification with a converging lens:
a – magnification means the image is inverted
a + magnification means the image is upright
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VI. REFLECTION
For a REFLECTED RAY, the angle of incidence = angle of reflection. This is
sometimes called the “law of reflection”
Just like for refracted rays, reflected ray angles are measured with respect to the
normal of the reflecting surface
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VII. MIRRORS
A.  PLANE or FLAT MIRROR
A plane mirror will provide a reflected VIRTUAL image behind the plane of the mirror
and the image will be upright and the same size as the object.
For mirror
analysis,
your eye will
be on the
same side as
the object
(of course!)
To find the image, the
rays of reflected light
are extended forward. The
point at which two (or more)
extended lines cross
show where the image
is located.
notice the little dotted lines normal to the mirror surface. Those help you
draw the reflected ray angle properly.
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B. CONCAVE MIRRORS
IF THE OBJECT IS OUTSIDE THE FOCAL POINT, THE IMAGE WILL BE REAL AND INVERTED.
IF THE OBJECT IS INSIDE THE FOCAL POINT. THE IMAGE WILL BE VIRTUAL AND UPRIGHT
THE FOCAL POINT AND THE CENTER OF CURVATURE ARE IN FRONT OF THE MIRROR.
Use 3 rays for the ray diagram.
A ray parallel to the principle axis reflect THROUGH the FOCAL POINT
A ray THROUGH the center of curvature goes THROUGH the IMAGE
A ray THROUGH the focal point reflects back PARALLEL to the axis.
THESE THREE RAYS INTERSECT AT THE IMAGE LOCATION
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concave mirrors, continued
object
virtual image
in the case of the object being inside of the focal point, the image is located
by extending the incident rays through the mirror surface.
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B. CONVEX MIRROR
CONVEX MIRRORS ALWAYS FORM VIRTUAL IMAGES BEHIND THE MIRROR.
THE FOCAL POINT AND THE CENTER OF CURVATURE ARE BEHIND THE MIRROR.
Draw 3 rays.
One parallel to the axis
One through the center of curvature
One through the focal point.
C
“OBJECTS IN MIRROR ARE CLOSER
THAN THEY APPEAR” 
For convex mirrors, the image is located by extending the reflected rays through the
mirror surface. The extended lines cross at the image location.
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