Reectiony Refraction and the Prism uMaterial tak en from
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Reectiony Refraction and the Prism uMaterial tak en from

Opticsy by E Hechty 5th Ed64257y Ch 5y 6v Huygens principle can be used to determine arious xperimentally eri64257able and predictable beha vior of the path of light through an optical system Ho we er as seen in the chapter on Lighty the Huygens efr

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Reectiony Refraction and the Prism uMaterial tak en from

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Reflectiony Refraction and the Prism uMaterial tak en from. Opticsy by E Hechty 5th Edfiy Ch. 5y 6v Huygens principle can be used to determine arious xperimentally erifiable and predictable beha vior of the path of light through an optical system Ho we er as seen in the chapter on Lighty the Huygens efront construction can be become complicatedy especially in systems with lar ge number of optical components simpler approach to track the beha vior of light is based on the propag ation of light rays based on some wellzdefined optics la ws 2 Law of

eflection When light tra elling in medium with inde is incident at an interf ace and some of it is scattered into medium then the phenomenon is kno wn as reflection forms of reflecz tion are generally recognized The first is dif fuse scattering or reflection in which the reflected light direction is unpredictable or random with respect to the incident direction The second is specular reflection in which the incident and scattered light ha wellzestablished relation with respect to direction Referring to Fig 2y when light is incident on surf ace making

an angle with the surf ace normaly it is reflected at an angle with respect to the normal In the case of specular reflectiony In additiony another important property of this reflection is that the incident and reflected rays lie on the same plane kno wn as the plane of eflection These tw properties define the law of eflection Figure 2. Specular eflection of light at smooth interface separ ating mediums and and epr esent the incident and eflected beams while is the tr ansmitted or efr acted beam. Accor ding to the laws of eflection I,

and the surface normal, lie on single plane the plane of reflection and the incident and eflected angles ar identical. 3 Snell law of efr action In the chapter on lightzmatter interaction we sa that when light entering medium with dif ferent refracti inde xy it bends This refraction or the amount of bending can
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Optics PHY 427 Refraction and the Prism be quantitati ely estimated by the Snell la ith reference to Fig ray tra elling in medium is incident at an angle and is transmitted into medium and at an angle with respect to the normal Snell la defines the

relation between the tw angles for an pair of media as. sin sin u2v Figure 3. Refr action of light and Snell law Light incident at an angle at the interface separ ating two media and is tr ansmitted into medium at angle determined by Eq. 1. By the use of these simple la ws and ray diagrams in combination with the la ws of dispersiony numer ous problems in olving the passage of light through matter and through arious optical componentsy lik prismsy lensesy microscopesy telescopesy etc can be aluated first discuss the interesting refracti and dispersi properties of prism Prism Ne wton

demonstrated in the 2711 that white light passing though prism could be separated into its dif erent colors While at that time he belie ed in the corpuscular theory of lighty we kno no that these indi vidual colors represent dif ferent elengths or frequencies From our introduction to refraction it is to be xpected that light of dif ferent colors will bed through dif ferent angles ith reference to Fig 4y white light tra elling in medium is incident at an angle to the normal of one ace of the prism ha ving refracti inde prism can serv man purposesy including as dispersi elementy beamsplitter and

polarizing de vice Here we discuss the beha vior of general disper sive prism as sho wn in Fig 4 The incident light is refracted at the first interf ace and tra els at angle with respect to the normal This light is incident at the second ace of the prism at an angle and finally refracted ag ain to xit the prism at angle The arious important angles in the ensuing discussion are. De viation angle This is defined as the angle between the original incident beam and the final transmitted beam u3v
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Optics PHY 427 Refraction and the Prism Figure 4. White light

incident on disper sive prism is efr acted and under certain conditions, its individual components can be seen. Prism angle The ape angle of the prism is kno wn as the prism angle Referring to fig and using geometry we can relate and as follo ws. In polygon abcdy there are tw right anglesy abc and ad Also for the polygony since the sum of opposite angles should be 180 so. bcd 180 u4v Further in triangle bcd we ha e. bcd 180 u5v and thereforey from eq and we ha e. u6v Thereforey using eq and 6y we can relate and as. u7v Using these relationsy you will perform arious xperiments and

aluation in xperiment ifie the prism spectrometer includingy observing the dispersi properties of the prismy measurement of refracti inde as function of elength and the minimum de viation position for the prism 1.1 Minimum de viation min and efracti index of the prism When the prism is rotated perpendicular to the plane of incidencey ifie such that the incidence angle is aried continuously the de viation of the transmitted light changes This de viation goes through minimum min The measurement of this angle is useful as it leads to simple relation between the refracti inde of the

prism and easily measurable quantities lik the prism angle This relation can be xtracted on the basis of complicated math or by using simple ph ysical ar guments Here we choose an ar gument based on symmetry By symmetry we can ar gue that the minimum de viation position should be independent of the
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Optics PHY 427 Refraction and the Prism Figure 5. Calculating the esolving power of prism. The various angles, including the de viation angle (D) and prism angle (A) ar indicated. direction in which light enters the prism In other ordsy light entering the prism from the left or

right should xhibit the same properties of refractiony minimum de viationy etc Thereforey if we re erse the direction of lighty thus ha ving the ne incident light new ol then new ol Experimentally it is observ ed that min occurs when the refracted ray inside the prism mak es equal angles with the tw aces This means that if we re erse the direction in which light is incident on the prismy we ha ne at which the min occurs Ho we er xperimentally only one min occurs and therefore. at min u8v Using Snell la we ha e. sin sin Using eq at minimum de viation we ha e. min or min and from eq and using

the minimum de viation conditiony eq 8y we get. A/ with the result that the refracti inde of an unkno wn prism can be obtained from. sin min sin u9v
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Optics PHY 427 Refraction and the Prism 1.2 Dispersion and esolving po wer As we kno aries with uor and the prism can be used to measure this ariation or disper sion measure of ho well the prism disperses the arious elengths is kno wn as the hr omatic esolving power of the prism Quantitati ely it is defined as where is an elength and is small dif ference centered around this elength ith reference to fig 5y consider

parallel beam of white light uas will be the case from the collimator used in xpt incident on the prism from the left When the beam emer ges on the righty an tw components ha ving elengths and will be separated by an angle or the rays emer ging from the top of the prismy the dif ference in lengths tra elled for the tw colors is and is mainly in the ambient medium Ho we er for the rays xiting from the bottom of the prismy the dif ference arises mainly because of tra el through the length of the base of the prism LsinA/ No since the optical path lengths of the tw beams are dif ferenty so the dif

ference at the bottom arises mainly sue to dif erence in the refracti indices of the tw colors and therefore. u0v No the smallest resolv able angley which will be quantitati ely discussed under the topic of dif fractiony is the dif fraction limited angle gi en by. where is the size of the aperture uor the beamv used to mak the measurement Using the definition of the resolving po wer we get. Lsin u21v where the ratio of the small dif ferences has been replaced by deri ati e Experimentally the resolving po wer xpressed by eq 21 requires an estimate of rate of change of the RfiI with

While this can be done using the general form of the dispersion relation deri ed in the chapter on Lightzmatter interactionsy more useful empirical form as established by Augustin Cauch and as gi en by. and hig her Wherey Ay By etc are Cauch constants unot to be confused with the prism angley etcfifiv In xperiment we will approximate to the second po wer in thus gi ving.