ANNOUNCEMENT. LECTURE 25 Spherical Refracting Surfaces

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ANNUNCEMENT Final: Thusday Dec 3, 208, 7 PM - 9 PM Location: Elliot Hall of Music Coves all eadings, lectues, homewok fom Chaptes 28 though 33 Multiple choice Pactice exams n the couse website and on

1 ANNUNCEMENT Final: Thusday Dec 3, 208, 7 PM - 9 PM Location: Elliot Hall of Music Coves all eadings, lectues, homewok fom Chaptes 28 though 33 Multiple choice Pactice exams n the couse website and on CHIP Bing you student ID cad and a one-page (twosided) cib sheet plus the oiginal (o evised) cib sheets fom Exams and 2 nly a few equations will be given The equation sheet that will be given with the exam is posted on the couse homepage - Link on the ight labeled Equationsheet It is you esponsibility to ceate you own cib sheet LECTURE 25 Spheical Refacting Sufaces

2 Geometic ptics When length scales ae >> than the light s wavelength, light popagates as ays incident ay eflected ay q q n Reflection: Refaction: q 2 efacted ay θ i = θ n sinθ = sinθ 2 If n > then q 2 > q If > n then q > q 2 Refacted ay bends away fom nomal Refacted ay bends towad the nomal Spheically Refacting Sufaces Refacted ay diected towad the cental axis A eal image will fom on that axis Refacted ay diected away fom the cental axis CANNT fom a eal image Backwad extension of the ay can fom a vitual image Real images Fomed when object is elatively fa fom efacting suface Vitual images Fomed when object is elatively nea efacting suface Real C I n s s Vitual I C n s s 2

3 Spheically Refacting Sufaces C I n Real > n Bends towad nomal Real image fomed s s Real n > Bends away fom nomal Real image fomed n C I s s Spheically Refacting Sufaces Vitual I C n > n Bends towad nomal but away fom cental axis Vitual image fomed n > Bends away fom nomal and cental axis Vitual image fomed Vitual C I n 3

Refacting Suface Fomula A point object is placed on the cental axis of a convex efacting suface Cente of cuvatue of the suface is at C Use small angle appoximation If q<< in adians, then sinq q.

4 Refacting Suface Fomula A point object is placed on the cental axis of a convex efacting suface Cente of cuvatue of the suface is at C Use small angle appoximation If q<< in adians, then sinq q. >% accuacy fo q<20 θ = α + β, β = θ 2 + γ n sinθ = sinθ 2 n θ θ 2 n α + γ = ( n )β α l s β l γ l s ' n s + s ' = n >n Sign Conventions fo Refacting Sufaces bjects on incident-light side s is positive Images on efacted-light side s is positive Cente of cuvatue on efacted-light side is positive Paametes ae negative if they don t meet above citeia fo being positive Real C I n s s 4

Summay: Spheically Refacting Sufaces. Real Images fom on the side of a efacting suface that is opposite the object 2. Vitual Images fom on the same side as the object 3.

5 Summay: Spheically Refacting Sufaces. Real Images fom on the side of a efacting suface that is opposite the object 2. Vitual Images fom on the same side as the object 3. Fo light ays making only small angles with the cental axis: n s + s ' = n 4. When the object faces a convex efacting suface, the adius of cuvatue is positive 5. When object faces a concave suface, adius of cuvatue is negative Example: Mosquito in Ambe A mosquito is embedded in ambe with an index of efaction of.6. ne suface of the ambe is spheically convex with a adius of cuvatue 3.0 mm. The mosquito head happens to be on the cental axis of that suface, and when viewed along the axis appeas to be buied 5.0 mm into the ambe. How deep is it eally? Daw a Pictue Vitual I C n 5

6 Example: Mosquito in Ambe s i = -5 mm bject and image ae on same side of efacting suface (vitual image) n =.6 Convention that object is in medium with index n = (ai) = -3 mm Negative because the object faces a concave suface Vitual I C n n + = n s o s i.6 + s o 5 =.6 3 s 0 = 4 mm Refacting Suface: Example Conside n =.0, =.8 = 0 cm s = 5 cm.0 5cm +.8 s.8 s =.8.0 0cm = ( )cm.8 s = = +35cm 0.333cm y s n s + s ' = n = 0.08cm C q q 2 Magnification (single suface) Small angle appoximation tanθ θ = y s n θ θ 2 M = y ' y = n s ' s = tanθ 2 θ 2 = y ' s ' 35cm.8(5cm) = 5 Image is eal, inveted and M > object n y' s 6

Definition Thin Lenses A lens is a tanspaent object with two efacting sufaces whose cental axes coincide (= the cental axis of the lens) Types Conveging lens: causes ays initially paallel to the

7 Definition Thin Lenses A lens is a tanspaent object with two efacting sufaces whose cental axes coincide (= the cental axis of the lens) Types Conveging lens: causes ays initially paallel to the cental axis to convege Diveging lens: a lens that causes ays initially paallel to the cental axis to divege Thin lens A lens whose thickest pat is thin compaed to the object distance, the image distance, and the adii of cuvatue of the two lens sufaces Thin Lenses: Conveging Lens C 2 F F 2 C 2 f Paallel ays efact twice Convege at F 2 a distance f fom cente of lens F 2 is a eal focal point because ays pass though f > 0 fo eal focal points f = s + Thin lens fomula s ' f = (n ) Lens make s 2 fomula n > 0 since n glass > n ai > 0 2 < 0 since object facing convex suface since object facing concave suface 7

8 Thin Lenses: Diveging Lens f < 0 fo vitual focal points C F 2 F C 2 f Extension 2 Rays divege, neve pass though a common point F 2 at a distance f F 2 is vitual focal point Thin Lenses A Double convex B Double concave Meniscus lens 2 /2 of A o B would be a plano-convex o plano-concave lens 8

9 Demo Lens boad conveging diveging Images fom Thin Lenses C 2 F C I 2 f s s Convex lens bject outside focal point Image is eal and inveted Magnification Same as fo mios M = y ' y = s ' s 9

10 Images fom Thin Lenses I F f s Convex lens bject inside focal point Image is vitual and same oientation as object s Images fom Thin Lenses C F 2 C 2 s s 2 Concave lens bject inside o outside focal point Image is vitual and same oientation as object 0

11 Popeties of Images Conveging Lenses (f>0) bject inside the focal point Image is vitual (s < 0), enlaged, has the same oientation, and fathe fom the lens bject outside the focal point Image is eal (s > 0, meaning on the othe side of the lens), inveted, educed o enlaged (depending on the object distance), and close to o fathe fom the lens. (like mio) Fo magnification = (-), s = s = 2f (like mio) bject at the focal point No image is fomed: a (diffeent) paallel bundle of ays is fomed fom each point of the object, and s (o s) = infinity Popeties of Images Diveging Lenses (f<0) bject inside o outside focal point Image is always vitual (s < 0), educed, has the same oientation, and close to the lens

12 Special Rays fo Refacting Sufaces Paallel ay Initially paallel to the cental axis Refacted ay passes though the 2 nd focal point Focal ay Passes though the st focal point Refacted ay is paallel to the cental axis Cental ay Passes though the cente of the lens Refacted ay popagates along the same diection as the incident ay Woks in eithe diection, of couse Locating Images by Dawing Rays F 3 2 F 2 I. Ray (paallel ay) passes though F 2 2. Ray 2 (focal ay) emeges paallel to the cental axis 3. Ray 3 (cental ay) emeges with no change in diection ay encountes the two sides of the lens whee they ae almost paallel 2

13 Locating Images by Dawing Rays 2 F I 3 F 2. Ray (paallel ay) will pass though F 2 2. Backwad extension of ay 2 (focal ay) passes though F 3. Ray 3 (cental ay) will emege with no change in diection Locating Images by Dawing Rays F 2 I F 2 3. Backwad extension of ay (paallel ay) passes though F 2 2. Extension of ay 2 (focal ay) passes though F 3. Ray 3 (cental ay) will emege with no change in diection 3

14 Note: If image is located beyond lens 2, s 2 fo lens 2 is negative Two Lens System Lens Lens 2 Let s epesent distance fom object,, to lens. Find s using: Ignoe lens. Teat Image as fo lens 2. Use s 2 = s. veall magnification: s = + f s s ' = + f 2 s 2 s 2 ' M = m m 2 = s ' s 2 ' s s 2 Example: Two Lens System Lens Lens 2 f f 2 A seed is placed in font of two thin symmetical coaxial lenses (lens & lens 2) with focal lengths f =+24 cm & f 2 =+9.0 cm, with a lens sepaation of L=0.0 cm. The seed is 6.0 cm fom lens. Whee is the image of the seed? Lens : = + f s s ' s ' = 8.0cm s L Image is vitual 4

15 Example: Two Lens System Lens Lens 2 f f 2 Lens 2: Teat image as 2 fo lens 2. 2 is outside the focal point of lens 2. So, image 2 will be eal & inveted on the othe side of lens 2. s 2 = L + s ' = 8cm s L = + f 2 s 2 s 2 ' s 2 ' = 8.0cm Image 2 is eal Table fo Lenses Lens Type bject Location Image Location Image Type Image ientation Sign of f, s, m Conveging Inside F Same side as object Conveging utside F Side of lens opposite the object Diveging Anywhee Same side as object Vitual Same as object +, -, + Real Inveted +, +, - Vitual Same as object -, -, + 5

LECTURE 25 Spherical Refracting Surfaces. Geometric Optics

$LECTURE 25 Spherical Refracting Surfaces. Geometric Optics$ LECTURE 25 Spherical Refracting Surfaces Geometric ptics When length scales are >> than the light s wavelength, light propagates as rays incident ray reflected ray θ θ r θ 2 refracted ray Reflection: Refraction: