Geometrical Optics and Refractive Index

Transcription

1 Geomercal Opcs and Refracve Index Please do no scrach, polsh or ouch he surface of he mrror. Inroducon You can fnd opcal phenomena wh mrrors, lenses, and he oher meda, such as waer. One of he fundamenal laws wh a plane mrror s known as he law of reflecon. Ths can be seen when you look yourself no a wall mrror n your daly lfe, whch explans ha you fnd yourself n he mrror as he same sze; and even hough s half of your hegh, you can see enre yourself n he mrror. Curved ypes of mrrors are convex and concave mrrors, whch are used n varous places, such as, n cars, medcal or denal purposes, cosmec mrrors, ec. The mporan parameers are known as he focal lengh and radus of curvaure, whch deermnes he feaure of he mrror. There s a relaonshp beween he focal lengh and s radus of curvaure: R = 2f where R s he radus of curvaure and f s he focal lengh. You may have an experence when lookng n waer he deph of he appearance s dfferen from he acual deph. Ths s caused by he refracon of lgh n a dfferen medum. Ths can be explaned by Snell s law. The formula s gven as n1 sn θ = n2 sn θ where n 1 and n 2 are he ndces of refracon for each medum and θ and θ are he angles for he ncden and ransmed lgh. The ray racng of lenses s fundamenally explaned by he Snell s law, bu he praccal properes of lenses can be llusraed by focal lenghs and oher relaed dsances. The basc ypes of hn lenses are convex and concave lenses. For daly lfe examples, a convex lens s used as a magnfyng glass, and a concave lens s used as a glass for nearsghedness. Objecve: To learn he concep of geomercal opcs (ray racng propery of lgh) To fnd he refracve ndex of acrylc rhombus (Snell's law) To see he properes of lenses and mrrors (law of reflecon, focal lenghs, ec.) 1. Plane mrror (he law of reflecon) If he plane s no a dffuse surface, he race of lgh s predcable, whch s known as he law of reflecon. The angles, θ and θ r, are called ncden and refleced angles, respecvely. Accordng o he law of reflecon, we always have θ = θ r. Noe ha he angles are aken from normal lne.

2 Procedure: 1 Place he ray box, label sde up, on a whe shee of paper on he able shown below. Adjus he sl so one whe ray s comng. 2 Use he plane surface of he mrror. Make an angle as shown below so ha boh he ncden and refleced rays are seen. 3 Mark he poson of he surface of he plane mrror. Trace he ncden and refleced rays wh arrows ndcang he ncomng and ougong rays. 4 On he paper, draw he normal o he surface as shown below. Use a proracor and be precse. 5 Measure he angle of ncdence (θ ) and he angle of reflecon (θ r ). (Make a large enough angle, θ, (more han 30 o ) o have a proper refleced angle, θ r.) Boh of hese angles mus be measured from he normal of he surface. Plane mrrors (The law of reflecon) [Measure hs by each n your group. If you are he only n he group, ry a leas wo measuremens.] 1 s 4 h Angle of Incdence, θ Angle of Reflecon, θ r % dfference θ θ r 100 (%) θ + θ / 2 ( ) r Queson: Are angles of ncdence and reflecon close o each oher? 2. Concave and convex mrrors The surface of he concave mrror consss of par of a crcle. The cener of he crcle called cener of curvaure, C, and s radus, R, are seen n he followng fgure. The mrror focuses he

3 ncomng parallel rays a he focal pon. The dsance beween he focal pon and he surface of he mrror s called focal lengh, f. The relaon beween R and f s R = 2f. Procedure: 1 Use fve whe rays from he ray box by adjusng he sl. Shne he rays sragh no he concave mrror as shown. Draw he surface of he mrror and race he ncden and refleced rays wh arrows (o show he approprae drecons.) Lgh Source 2 The place where he refleced rays cross each oher s he focal pon of he mrror. Measure he focal lengh, whch s from he cener of mrror s surface o he focal pon. 3 Use he compass o draw a crcle ha maches he curvaure of he mrror. Measure he radus of he curvaure usng a ruler. (Hn: Esmae he cener of curvaure from R=2f. Then, check f he curvaure fs wh he crcle you make by he compass.) [Measure hs by each n your group. If you are he only n he group, ry a leas wo measuremens.] Focal lengh, f Radus of curvaure usng compass, R 1 s 4 h Quesons: Does he equaon R=2f hold from your expermen?

4 How abou a convex mrror? How do you oban he focal lengh? Hypohesze he procedure. 3. Snell s law The formula s: n1 sn θ = n2 sn θ, where n s he ndex of refracon and he θ and θ are he corresponden angles. Procedure: 1 Place he ray box, label sde up, on a whe shee of paper on he able. Use only one whe ray by sldng he ray mask. 2 Place he rhombus on he paper and poson so he ray passes hrough he parallel sdes as shown below. (Make a large enough angle for θ so you can measure θ properly.) Normal o he surface Rhombus Incden ray Transmed ray 3 Mark he poson of he parallel surfaces of he rhombus and race he ncden and ransmed rays wh arrows n he approprae drecons. 4 Mark carefully where he ray eners and leaves he rhombus. Ths s very mporan because he ransmed ray canno be seen. 5 Remove he rhombus and on he paper draw a lne connecng he pons where he ray enered and lef he rhombus. Smulae hs n your mnd o avod a carefree msake. 6 A he pon where he ray eners he rhombus, draw he normal of he surface. 7 Measure he angle of ncdence θ and angle of refracon θ wh a proracor. Boh of hese angles mus be measured from he normal lne. Deermne he unceranes for he measuremen.

5 8 Calculae he ndex of refracon for he rhombus by usng he gven equaon. I should be close o 1.5. The rhombus s made of Acrylc whch has an ndex of refracon of Reference: for lgh of wavelengh 486 nm n a vacuum (blue), for wavelengh 589 nm (green), and for wavelengh 651 nm (red). Noce ha n general for vsble lgh, he ndex of refracon for Acrylc becomes larger wh ncreasng frequency. [Measure hs by each n your group. If you are he only n he group, ry a leas wo measuremens.] Angle of Incdence Angle of Refracon (θ ) (θ ) 1 s 4 h Average of he ndex of refracon Index of Refracon (n) For he rhombus Queson: Wha s he relaonshp beween he angle of ncdence and he angle of refracon? [When he θ ncreases, wll he θ be ncreased or decreased?] Queson: Is he ndex of refracon for he rhombus close o 1.5? 4. Convex and concave lenses The convex lens s also called a conversng lens. I depcs ha he lgh rays converge no one place, whch s he focal pon. The dsance beween he focal pon and he cener of he lens s known as focal lengh, f. Procedure: 1 Place he ray box on a whe paper. Use he fve whe rays from he ray box, and hen shne he rays sragh no he convex lens.

6 2 Trace around he surface of he lens and race he ncden and ransmed rays. 3 Wh he lens removed, mark he cener of he lens. 4 Fnd he focal pon of he lens. You may see he fuzzy nerval around where he focal pon should be. Mark he boundares of hs nerval o se your lms on he uncerany and ake he cener of he nerval o be your focal pon. 5 Measure he focal lengh, whch s from he cener of he lens o he focal pon. Don forge o deermne s uncerany. 6 Choose a new dsance and repea he above sep o see f he focal lengh changes. [Measure hs by each n your group. If you are he only n he group, ry a leas wo measuremens.] The dsance beween lens and lgh Focal lengh of he convex lens source ( f ± f ) 1 s 4 h Quesons: Does he focal lengh depend on he dsance beween lens and lgh source? Desgn an expermen where you oban he focal lengh of concave lens.