Optics

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Optics
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The electromagnetic spectrum Visible light make
up only a small part of the entire spectrum
of electromagnetic waves. Unlike sound waves and
mechanical waves, they don t require a material
medium for their transmission, they can propagate
through a vacuum. Electromagnetic waves consist
of time-varying electric and magnetic fields that
propagate perpendicular to each other and to the
direction of the propagation of the wave. All
electromagnetic waves travel at a fixed speed
through a vacuum regardless of their frequency.

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Dispersion and Refraction
Prisms display the phenomena called dispersion by
separating white light into components of
different wavelength (different colors). The
different colors refract at different angles,
splitting white light into a rainbow. When light
passes through a prism, it is refracted twice,
when it enters the prism and when it leaves.
Refraction is the change in direction of light as
it leaves one medium and enters a different
medium. Every medium has a characteristic value
called the index of refraction which is a value
used to give the ratio of the speed an
electromagnetic wave in vacuum to the speed of
the electromagnetic wave in a particular medium.
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Refraction Refraction is the slowing of light by
matter and it follows Snells Law. It is the
bending of any wave, such as a light or sound
wave, when it passes from one medium into another
of different optical density
Snell's law states that the ratio of the sines of
the angles of incidence and refraction is
equivalent to the ratio of velocities in the two
media or the ratio of the index of refraction for
the two media.
or
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Refraction of a spoon in a glass of water
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Snells Law
Normal
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Problem If a light beam makes an angle of 40º
with the surface, it makes an angle of 50º with
the normal this is the angle of incidence. We
can find the angle of refraction by using
Snells Law. Solution
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Magnification v is the distance from the lens to
the image. u is the distance from the lens to the
object. a is the height of the image, b is the
height of the object. Thin Lens Equation u is
the distance (measured along the axis) from the
image to the center of the lens The image is
real, inverted, and behind the lens if u is
positive. The image is virtual, upright, and in
front of the lens if u is negative.
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The approximation for thin lenses
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The thin-lens diagam is composed of three
rays Ray number 1.) A ray from the top of the
object parallel to the centerline and
perpendicular to the lends. It then travels
through the focal point on the other side of the
lens. Ray number 3.) A ray through the center of
the lens which won't be bent. Ray number 2.) A
ray through the focal ponit on the near side of
the lens.
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Problem An object of height 14 cm is placed 46 cm
in front of a converging lens with a focal
length of 26 cm. Where is the image? Is it real
or virtual? Is it upright or inverted? Whats the
height of the image? With u 46 cm and f 26
cm, the lens equation gives us Because v
is positive. the image is real. Real images are
inverted. The magnification is The height of
the image is given by
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Huygens Principle
Every point of a wave front can be considered the
origin of a new circular or spherical wave, the
so-called elemetary wave. The new position of the
wave front results from the superposition of all
of the elementary waves. The Huygens wave front
is a series of concentric circles originating
from the points on a wave front.
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Diffraction in a Single Slit
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If a wave front goes through a single slit, it
breaks down into individual circular waves
called elementary waves. As we know through
Huygens Principle, the single slit acts a point
source for a new circular or spherical wave. This
phenomena is called diffraction. The difference
between refraction and diffraction
In refraction, the wave is being bent because the
speed of propagation in the medium it is moving
into is different than the medium it is moving
out of. For instance, light moving from air to
water at an angle is bent away from the axis that
runs perpendicularly to the surface because light
travels slower in water than in air. In
diffraction, the wave is being bent (often times
through very small slits) when it hits somthing,
causing a diffraction pattern to form.
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Double Slit Interference
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Double Slit Interference
source
screen
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If the crests and troughs of the two waves arrive
at the screen at the same time, then the waves
interfere constructively and a bright band
appears on the screen. If the crest of one wave
arrives at the same time as the trough of the
other wave, then the waves interfere
destructively and cancel each other out. This
area of the screen will be dark. If the distance
to the screen D is much larger than the distance
between the stripes, the conditions for bright
or dark bands are

bright bands dark bands

where is the wavelength of the
light, d is the separation between the two slits
and n is the order of maximum observed (central
maximum is n 0)
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Problem When sodium yellow light ( 589 nm) is
used in a double slit experiment, the first order
maximum is 0.035 cm from the central maximum.
When another light source of unknown wavelength
is used. The first order maximum occurs at 0.03
cm from the center. What is this wavelength?

and , thus