study of reflection and refraction of light

8/8/2019 Study of Reflection and Refraction of Light

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STUDY OF

REFLECTION ANDREFRACTION OF

LIGHTIMAGE FORMATION BY MIRROR, LENS ETC

THIS REPORT CONSIST OF DETAILS ABOUT THE IMAGE FORMATION AND

BEHAVIOUR OF LIGHT .

2010SHEIKH MD ASHRAFUL ISLAM

SCHOOL OF ENGINEERING AND TECHNOLOGY

3/12/2010


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Law of Reflection


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A light ray incident upon a reflective surface will be reflected at an angle equal to the incidentangle. Both angles are typically measured with respect to the normal to the surface. This law ofreflection can be derived from Fermat's principle.

The law of reflection gives the familiar reflected image in a planemirror where the image distance behind the mirror is the same asthe object distance in front of the mirror.

Fermat's Principle:ReflectionFermat's Principle: Light follows the path of least time. The law ofreflection can be derivedfrom this principle as follows:

The pathlength L from A to B is

Since the speed is constant, the minimum time path is simplythe minimum distance path. This may be found by setting thederivative of L with respect to x equal to zero.


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This derivation makes use of the calculus ofmaximum-minimum determination, the derivativeof a square root, and the definitions of the triangle trig functions.

Mirror Geometry

Mirror Ray TracingMirrors are used widely in optical instruments for gathering light and forming images since theywork over a wider wavelength range and do not have the problems of dispersion which are

associated with lenses and other refracting elements.


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Mirror InstrumentsMirrors are widely used in telescopes and telephoto lenses. They have the advantage of operatingover a wider range of wavelengths, from infrared to ultraviolet and above. They avoid thechromatic aberration arising from dispersion in lenses, but are subject to other aberrations.Instruments which use only mirrors to form images are called catoptric systems, while thosewhich use both lenses and mirrors are called catadioptric systems (dioptric systems being thosewith lenses only).

Spherical Mirror EquationThe equation for image formation by rays near the optic axis (paraxial rays) of a mirror has thesame form as the thin lens equation:


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Using a ray parallel to the principal axis and one incident upon the center of the mirror, theposition of the image can be constructed by back-projecting the rays which reflect from themirror. The virtual image that is formed will appear smaller and closer to the mirror than theobject.

Concave Mirror Image

If the object is outside the focal length, a concave mirror will form a real, inverted image.


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Refraction of LightRefraction is the bending of a wave when it enters a medium where it's speed is different. Therefraction of light when it passes from a fast medium to a slow medium bends the light raytoward the normal to the boundary between the two media. The amount of bending depends onthe indices of refraction of the two media and is described quantitatively by Snell's Law.

Refraction is responsiblefor image formation by

lenses and the eye.

As the speed of light is reduced in the slower medium, the wavelength is shortenedproportionately. The frequency is unchanged; it is a characteristic of the source of the light andunaffected by medium changes.

Image Formation


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Thin Lens EquationA common Gaussian form of the lens equation is shown below. This is the form used in mostintroductory textbooks. A form using the Cartesian sign convention is often used in moreadvanced texts because of advantages with multiple-lens systems and more complex opticalinstruments. Either form can be used withpositive ornegative lenses and predicts the formationof both real and virtual images. Does not apply to thick lenses.

Enter data below, then click on the quantity you wish to calculate in the active formula above.

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For a lens of focal length f= cm,

corresponding to lens powerP = diopters,

an object distance ofo = cm

will produce an image at i = cm.

The linear magnification will be M =Bottom of Form

If the lens equation yields a negative image distance, then the image is a virtual image on thesame side of the lens as the object. If it yields a negative focal length, then the lens is a diverging

lens rather than the converging lens in the illustration. The lens equation can be used to calculatethe image distance for either real or virtual images and for either positive on negative lenses. Thelinear magnification relationship allows you to predict the size of the image.


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Thin-Lens Equation:Cartesian ConventionThe thin-lens equation in the Gaussian form is

where the Cartesian sign convention has been used. The lens equation is also sometimesexpressed in the Newtonian form. The derivation of the Gaussian form proceeds from trianglegeometry. For a thin lens, the lens power P is the sum of the surface powers. For thicker lenses,Gullstrand's equation can be used to get the equivalent power.

Snell's LawSnell's Law relates the indices of refraction n of the two media to the directions of propagation in

terms of the angles to the normal. Snell's law can be derived from Fermat's Principle or from theFresnel Equations.

Enter data below, then click the symbol of the quantity you wish to calculate.

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Indices of refraction: Angles with surface normal:


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=

=

=

=

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Enter data and then click on the symbol for the quantity you wish to calculate in the activeequation above. The numbers will not be forced to be consistent until you click on the quantity tocalculate. Indices of refraction must be greater than or equal to 1, so values less than 1 do notrepresent a physically possible system.

If the incident medium has the larger index of refraction, then the angle with the normal isincreased by refraction. The larger index medium is commonly called the "internal" medium,since air with n=1 is usually the surrounding or "external" medium. You can calculate thecondition fortotal internal reflectionby setting the refracted angle = 90 and calculating the

incident angle. Since you can't refract the light by more than 90, all of it will reflect for anglesof incidence greater than the angle which gives refraction at 90.

Total Internal ReflectionWhen light is incident upon a medium of lesserindex of refraction, the ray is bent away from thenormal, so the exit angle is greater than the incident angle. Such reflection is commonly called"internal reflection". The exit angle will then approach 90 for some critical incident angle c ,and for incident angles greater than the critical angle there will be total internal reflection.

The critical angle can be calculated from Snell's law by setting the refraction angle equal to 90.Total internal reflection is important in fiber optics and is employed inpolarizing prisms.


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For any angle of incidence less than the critical angle, part of the incident light will betransmitted and part will be reflected. The normal incidence reflection coefficient can becalculated from the indices of refraction. For non-normal incidence, the transmission andreflection coefficients can be calculated from the Fresnel equations.

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For total internal reflection of light from a medium of index of refraction

n1 = ni = ,

the light must be incident on a medium of lesser index. If the new medium has

n2 = nt =

then the critical angle for internal reflection is c = degrees.

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If values for n1 and n2 are entered above, the critical angle c for total internal reflection will becalculated. (For example, c = 48.6 for water and air.) But the angle for total internal reflectioncan be measured and used to determine the index of refraction of a medium. If a new value of cis entered above, then the corresponding value of n1 will be calculated.


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Ray Diagrams for LensesThe image formed by a single lens can be located and sized with three principal rays. Examplesare given for converging and diverging lenses and for the cases where the object is inside and

outside the principal focal length.

The "three principal rays" which are used for visualizing the image location and size are:

1. A ray from the top of the object proceeding parallel to the centerline perpendicular to thelens. Beyond the lens, it will pass through the principal focal point. For a negative lens, itwill proceed from the lens as if it emanated from the focal point on the near side of thelens.

2. A ray through the center of the lens, which will be undeflected. (Actually, it will bejogged downward on the near side of the lens and back up on the exit side of the lens, butthe resulting slight offset is neglected for thin lenses.)

3. A ray through the principal focal point on the near side of the lens. It will proceed parallel

to the centerline upon exit from the lens. The third ray is not really needed, since the firsttwo locate the image.

Ray Diagrams for Convex Lenses


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For an object outside the focal point, a real inverted imagewill be formed.

4.

For an object inside the focal point, avirtual erect image will be formed

Ray Diagrams for Concave LensesThe ray diagrams for concave lenses inside and outside the focal point give similar results: anerect virtual image smaller than the object. The image is always formed inside the focal length ofthe lens.

Ray Diagram for Two Lenses
http://hyperphysics.phy-astr.gsu.edu/hbase/geoopt/image2.html#c3http://hyperphysics.phy-astr.gsu.edu/hbase/geoopt/image2.html#c2http://hyperphysics.phy-astr.gsu.edu/hbase/geoopt/image.html#c1


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PrismsA refracting prism is a convenient geometry to illustrate dispersion and the use of the angle ofminimum deviationprovides a good way to measure the index of refraction of a material.Reflecting prisms are used for erecting or otherwise changing the orientation of an image andmake use oftotal internal reflection instead ofrefraction.


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White light may be separated into its spectral colorsby dispersion in a prism.

Prisms are typically characterized by their angle of minimum deviation . This minimumdeviation is achieved by adjusting the incident angle until the ray passes through theprismparallel to the bottom of the prism.

An interesting application of refraction of light in a prism occurs in atmospheric optics when tinyhexagonal ice crystals are in the air. This refraction produces the 22 halo commonly observed innorthern latitudes. The fact that these ice crystals will preferentially orient themselveshorizontally when falling produces a brighter part of the 22 halo horizontally to both sides ofthe sun; these bright spots are commonly called "sundogs".

The angle of minimum deviation for aprism may be calculated from the prism equation. Notefrom the illustration that this minimum deviation occurs when the path of the light inside the

prism is parallel to the base of the prism. If the incident light beam is rotated in either direction,the deviation of the light from its incident path caused by refraction in the prism will be greater.

White light may be separated into its spectral colorsby dispersion in a prism.

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Fiber Optic ImagingFiber optic imaging uses the fact that the light striking the end of an individual fiber will be

transmitted to the other end of that fiber. Each fiber acts as a light pipe, transmitting the lightfrom that part of the image along the fiber. If the arrangement of the fibers in the bundle is keptconstant then the transmitted light forms a mosaic image of the light which struck the end of thebundle.

study of reflection and refraction of light

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