REFRACTION. a. To study the refraction of light from plane surfaces. b. To determine the index of refraction for Acrylic and Water.

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1 Purpose Theory REFRACTION a. To study the refracton of lght from plane surfaces. b. To determne the ndex of refracton for Acrylc and Water. When a ray of lght passes from one medum nto another one of dfferent optcal densty, t undergoes a change of velocty and a consequent change n drecton. Fgure s an example of refracton. The ncdent ray makes an angle wth the normal to the refractng surface called the angle of ncdence,. The refracted ray makes an angle wth the normal to the refractng surface called the angle of refracton, r. In Fgure, f the ncdent medum s vacuum or free space, the speed of lght s c. (The speed of lght n ar s very nearly equal to that n vacuum.) If the speed of lght n the refractng medum v s less than the speed of lght n the ncdent medum, the refracted ray bends towards the normal so that angle r s less than angle. (If the speed of lght v n the ncdent medum s less than that of the speed of lght n the refractng medum, the refracted ray would bend away from the normal. Ths can be seen n Fgure f the lght path s reversed. The refracted ray now becomes the ncdent ray, and the ncdent ray s now the refracted ray, bendng away from the normal.) Snell s Law: If the ncdent medum s a vacuum (or ar, approxmately), the basc law of refracton s Snell s Law accordng to whch c () r v The rato c/v s called the ndex of refracton, n, of the refractng medum: n c / v () Thus, Snell s Law may be wrtten as Incdent medum = VACUUM Speed of lght = c Refractng medum = ACRYLIC Speed of lght = v v < c Fg.. The refracton of lght as t passes from vacuum nto Acrylc. n (3) r r Brooklyn College

2 It s therefore possble to characterze a medum va ts ndex of refracton by measurng the angles of ncdence and the angle of refracton r. Fnally, when lght passes from one medum to the next, ts frequency f does not change. The electrons n the refractng medum absorb energy from the lght and undergo a vbratonal moton wth the same frequency. The moton of the electrons then causes reradaton of the energy wth the same frequency. In any medum v = λ f. ce the speed of lght n the refractng medum v s less than the speed of lght c n vacuum, and ts frequency f s unchanged, ts wavelength λ s correspondngly reduced. Hence, the wavelength λ of lght n a materal s less than the wavelength λ 0 of the same lght n vacuum by a factor of n: o. (4) n Experment: There are three parts to the experment to study the refracton of lght and determnaton of the ndex of refracton. In Part I we wll use an acrylc slab, part II a prsm, and part III a jar of water. You are provded wth the followng apparatus. Apparatus Rectangular Acrylc plate, Acrylc prsm, protractor, ruler, Cork board, whte paper, Red Laser. Descrpton of Apparatus a. Acrylc slab c. Red laser d. Water tank wth sldng plates a. Prsm Fg. : Apparatus for the experments n ths lab You wll use an acrylc slab (Fg. a) and prsm (Fg. b) to study the refracton of lght from ther surfaces to determne the ndex of refracton of the materals used to make the slab and prsm by measurng the angles of ncdence and refracton. The beam of a laser (Fg. c) s used to trace the drecton of lght. You wll also use a water jar to determne the ndex of refracton of water usng an apparatus shown n Fg. d. Brooklyn College

3 Procedure Part I. Refracton by a rectangular Acrylc plate. Place a sheet of paper on the cork board, and on t the rectangular Acrylc plate. Carefully trace out the outlne of the plate.. Place the laser on the bench table, not on the cork board. Shne the laser beam on the top vertcal surface of the plate at some ncdent angle. Wth your pencl, mark two ponts A and B along the ncdent beam, one near the plate and the other about 5 cm from t. See Fgure 3. Do the same wth the emergent beam, ponts C and D. Pont C s near the plate. See Fgure 3. ** Turn off the Laser when not n use ** Incdent ray B ar A r Refracted ray r Acrylc ar C e Emergent ray D Fg. 3. Refracton by a rectangular Acrylc plate. 3. Now remove the plate from the paper. Wth the protractor, draw a perpendcular at ponts A and C. Wth the ruler, draw the ncdent, refracted and emergent beams. Wth the protractor, measure the angles, r, r, e. Repeat the experment for two other ncdent angles. Then from Snell s Law, the ndex of refracton of the Lucte plate s e n (5) r r Record the data n Table I. Brooklyn College 3

4 Part II. Refracton by a prsm (a) Place the prsm n the center of a sheet of paper on the cork board. Trace the outlne of the prsm. Mark off two ponts E and F on sdes AB and AC of the prsm that are equdstant from the vertex A. (See Fgure 4.) Wth the laser on the bench table, shne the beam at the pont E on sde AB. Adjust the angle of ncdence of the beam such that the emergent ray emerges from pont F on the sde AC. Mark off two ponts J and K about 5 cm from ponts E and F along the ncdent and emergent beams, respectvely. m Fg. 4 Refracton by a Acrylc prsm. Now remove the prsm from the paper. Wth the protractor, draw a perpendcular at ponts E and F. (See Fgure 4.) Wth the ruler, draw the ncdent, refracted and emergent beams. Extend the ncdent beam JE to H. Extend the emergent beam FK backwards to L. Wth the protractor, measure the angles, r, r, e the vertex angle α and the angle of mnmum devaton θ m. As shown below, the ndex of refracton n as obtaned from Snell s Law can also be expressed n terms of the angle of mnmum devaton θ m and the vertex angle α as m n (6) r Proof of ths equaton s gven n the appendx at the end of ths lab manual. Record the data n Table II. (b) We next wsh to show expermentally that θ m s the angle of mnmum devaton. Agan, on the paper, draw the outlne of the prsm, and mark off an arbtrary pont E along the sde AB. Then focus the laser beam on pont E but wth an ncdent angle that s greater than that that employed n Part (a). Mark the pont F on sde AC from whch the ray emerges. Mark off two ponts J and K about 5 cm from ponts E and F along the ncdent and emergent beams, respectvely. Brooklyn College 4

5 Remove the prsm, and wth the protractor, draw the normal at ponts E and F. Wth the ruler, draw the ncdent, refracted and emergent rays. Extend the ncdent ray JE to H. Extend the emergent beam FK backwards to L. Measure the angles, r, r, e and the angle of devaton θ (angle FGH) (See Fgure 4). Record the data, the value of the refractve ndex n, and the angle of devaton θ n Table III. (c) Repeat Part II (b) for an angle of ncdence that s less than that employed n Part (a). Part III. Refracton by water In ths fnal component of the experment, we wll determne the ndex of refracton of water. The apparatus used for ths part of experment s shown n Fgure 5. It has a Metal Frame contanng four brass slders,, 3, 4, and a jar of water. See Fgures 5 for the expermental setup. Brass slders 3 4 Frame Eye Water level Ar E Water Fg. 5a Expermental setup for refracton by water. Fg. 5b Brass slders n frame.. Set the slders n the slots of the frame wth the arrows pontng upwards, wth the correspondng numbers as shown n Fgure 5. Set the jar of water on a whte sheet of paper. Mount the metal frame on the jar as shown n Fgure 5a.. Push slder 4 as far down nto the water as possble. Push slders and 3 as close to the surface of the water as possble wthout touchng the water. Fnally adjust slder so that the pont A appears to be n lne wth ponts B and D. See Fgure 5a. To confrm your sghtng, shne the laser beam along the lne AB. You should see the beam reflected at D. 3. Remove the frame from the water and lay t on a sheet of paper wthout dsturbng the slders. Mark the postons of the ponts A, B, C, D on the paper. You must nclude ths work n your report after further drawng and calculaton. Brooklyn College 5

6 Computaton. Calculate the ndex of refracton of the plate from the data n Table for angles of ncdence, refracton, and emergence, and record n Table.. Calculate the ndex of refracton of the prsm from the data n Table for angles of ncdence, refracton, and emergence, and record n Table. Also calculate the ndex of refracton from the angle of mnmum devaton usng Eq Calculate the ndex of refracton of the prsm from the data n Table 3 for angles of ncdence, refracton, and emergent, and record n the Table 3. Determne the angle of devaton and compare ths angle wth the angle of mnm devaton obtaned n Part II (a). 4. For part III, once you have the marks of the slders on the paper, draw the lne BC (the water level). Wth the protractor erect a perpendcular to BC at B. Draw the lnes DB and AB. Fnally, measure the angles of ncdence and refracton r wth the protractor. Determne the ndex of refracton of water va Snell s Law. 5. Extend the lne of sght AB to D' on slder 4. The apparent poston of the edge of the slder 4 s at D'. Measure the apparent depth ED' and the true depth ED. Then from trangle BED' (see Fgure 5a) Questons ED' tan (90 ). (7) BE From trangle BED (see Fgure 5a) ED tan (90 r). (8) BE Then from Eqs. (7) and (8) we have ED' tan (90 ). (9) BE tan (90 r) Determne the rato ED'/ED from Eq. (9) and compare wth the rato of the measured dstances ED' and ED.. In Part I, s the emergent ray parallel to the ncdent ray? What causes, other than expermental error, wll make the emergent ray not parallel to the ncdent ray?. If you desre to shoot a fsh whose mage can be seen n clear water, should you am above or below the fsh? Explan by the ad of a dagram. Brooklyn College 6

7 Date experment performed: Name of the group members: Table. Tral 3 Incdent Refracted r Angles Incdent r Data Sheet Emergent e r Refractve Index n e r Average Table Vertex angle = Angle of mnmum devaton m = Angles Refractve Index n Incdent Refracted r Incdent r Emergent e r e r ( ) Average m Table 3 Incdent Angles Refractve Index, n Angle of Devaton Refracted Incdent Emergent e r r e r r Brooklyn College 7

8 Appendx: Proof: Dervaton of Eq. 6 for an sosceles prsm. The mnmum devaton n an sosceles prsm occurs when there s symmetrc refracton,.e., Angle = angle e ; angle r = angle r ; EF parallel to BC because r = r. ( r ) = ( r ) Normal ( r ) m Normal r r Incdent ray Emergent ray Fg. 6 Varous angles n the refracton by a prsm for mnmum devaton m. From Fg. 6 and the propertes of trangles, so that and ( r ), (0) m m r, () r 90, () because EF s parallel to BC and angle AEF =. A perpendcular bsector of BC passng through A bsects the angle of prsm n half, thus 90. (3) From Eqs. () and (3), r. (4) On substtutng Eq. (4) nto Eq. (), and then employng Eq. (), Snell s law becomes m n whch s Eq. (6). r Brooklyn College 8