I N V E S T I C E D O R O Z V O J E V Z D Ě L Á V Á N Í

Transcription

1 GEOMETRICAL OPTICS 1. Mirrors I N V E S T I C E D O R O Z V O J E V Z D Ě L Á V Á N Í their unction is bsed on the lw o relection types : plne curved relecting surces: ordinry metl lyer covered by glss protection (corrosion, scrtches) HQ specil metl lyer only better imge ) plne mirrors A A A... object A... imge... object distnce... imge distnce ( 0 virtul, 0 rel ) describe the imge: rel virtul mgniied diminished o the sme size upright (erect) inverted lterlly inverted b) curved mirrors ry digrms C... centre o curvture r... rdius o curvture... ocl length P... pole o the mirror (V) principl xis RAY COMING IS REFLECTED 1 through C through C 2 through F prllel to principl xis 3 prllel to principl xis through F 4 to P t the sme ngle concve mirror GEOMETRICAL OPTICS

2 convex mirror Sketch the ollowing situtions on n extr sheet o pper nd describe the imges 1. = 2.5 cm, ) = 6 cm, b) = 5 cm, c) = 3.5 cm, d) = 1 cm 2. = -3 cm, = 5 cm mirror ormul α α ρ σ σ r 1 1 = GEOMETRICAL OPTICS

3 3. Prove the precision o your sketches questions 1 nd 2 - using the mirror ormul. mgniiction ormule y M = y M 0... erect (virtul) M 0... inverted (rel) M 1... mgniied M 1... diminished 4. A concve mirror o ocl length 30 cm orms rel imge mgniied 10 times. Clculte the imge nd object distnce. L , 81, 83, GEOMETRICAL OPTICS

4 2. Thin lenses unction bsed on the lw o rerction dierent shpes CONCAVE thinner in the middle, 0 CONVEX, converging thicker in the middle, 0 ind nd sketch the ollowing shpes o lenses: biconvex plno-convex convex meniscus biconcve plno-concve concve meniscus lenses hve two ocuses F nd F The ocl lengths re equl or thin lenses only! r in generl TWO rdii o curvture!!! 2 power o lens bsolute rerctive index o the medium o the lens 1 n = n r1 r = ϕ POWER OF A LENS ocl.r.i. o the medium rdii o curvture length AROUND the lens (diicult sign convention positive result o the brcket or convex lens) [ ϕ ] = D (dioptre) GEOMETRICAL OPTICS

5 ry digrms RAY COMING IS REFRACTED 1 through O through O 2 through F prllel to principl xis 3 prllel to principl xis through F F F F F 5. Sketch the ollowing situtions nd describe the imges: 1. = 2 cm, ) = 4.5 cm, b) = 4 cm, c) = 3 cm, d) = 1 cm 2. = -4 cm, ) = 6 cm., b) = 2 cm GEOMETRICAL OPTICS

6 thin lens ormul mgniiction ormule 1 1 = + 1 y M = y!!! SIGN CONVENTION or POSITIVE when REAL (the sme s or mirrors), but REAL is BEHIND!!! NEGATIVE when VIRTUAL (the sme s or mirrors), but VIRTUAL is IN FRONT OF THE LENS!!! 6. Prove the results o previous sketches using the thin lens ormul nd mgniiction ormule. 7. A lens orms rel imge mgniied 3 times. When the object is moved BY 15 cm towrds the lens, the imge is 8 times mgniied. Clculte the ocl length o the lens. L687-91, 95, , 103, , The eye = cm (when ccommodted to ) ner point (NP) = 25 cm r point (FP) = distnce o most distinct vision d = 25 cm long sight 1 - FP t - NP urther thn 25 cm - correction convex lens 1 1 = + d NP 25 cm virtul imge t NP object distnce (negtive number!!!) short sight (krátkozrkost) ϕ = - FP closer thn t - NP 25 cm (or less) - correction concve lens = + = FP FP object t virtul imge t FP (negtive number!!!) GEOMETRICAL OPTICS

7 ϕ = = + d NP between 25 cm nd 0 8. Clculte the power o the humn eye 9. Eyes behind strong spectcles seem to be diminished or mgniied. Which disese nd correction does it correspond with? 10. Clculte the power o the lens ) SS, NP = 10 cm, b) LS, NP = 50 cm, c) SS, FP = 10 m test your vision - binoculr vision rolled pper - blind spot 6 7 cm - inverted imge on retin pin eye ocused to ininity through pin hole sheet o pper 4. Subjective opticl instruments orm virtul imges, which re objects or humn eye ngulr mgniiction τ ' γ = with the device τ without the device ) mgniying glss single converging lens Find nd lbel τ nd τ ' F d d γ (British eqn.: γ = + 1 s it depends on the position o the object nd the lens) mx. mgniiction is bout 6, when more thick lens distortion o the imge GEOMETRICAL OPTICS

8 b) compound microscope I N V E S T I C E D O R O Z V O J E V Z D Ě L Á V Á N Í consists o two (sets o) convex lenses - objective, which orms rel, mgniied nd inverted imge I 1 o n object O (plced just outside its ocus F o ). I 1 is just behind the ocus F e o the eyepiece, which cts s mgniying glss nd produces mgniied, virtul imge I 2. Sketch the optics o the microscope using dditionl mterils or the internet nd describe resultnt properties o the imge I 2 relted to the object O. British convention γ = m m e o mgniictions o the eyepiece nd the objective Czech convention distnce between d γ = 1 2 F1 F 2 c) telescopes consist o n objective (convex lens or concve mirror) which orms n imge t ocl plne (object is t ininity). The oci o the objective nd n eyepiece (convex or concve lens) coincide so the inl imge is ormed t ininity too, but s the ocl lengths dier, ngulr mgniiction is ormed. Kepler s telescope (stronomicl) 2 convex lenses Newtonin telescope (stronomicl) concve mirror + convex lens Glillein telescope convex + concve lens (shorter) terrestril telescope 2 convex lenses + erecting lens between which does NOT mgniy γ = o e Use dditionl mterils books, internet... to sketch the types o telescopes mentioned bove, describe the dvntgesdisdvntges nd use o ech type GEOMETRICAL OPTICS

9 L , GEOMETRICAL OPTICS

10 5. Objective opticl instruments I N V E S T I C E D O R O Z V O J E V Z D Ě L Á V Á N Í orm rel imges on screen, sensitive lyers o ilms etc. ) projector projection lens (convex) orms highly mgniied, rel nd inverted imge o slide (mster) high power lmp, relector nd condenser mke only the intense nd uniorm illumintion o the object ind ll the components on the igure below b) cmer objective consists o more lenses ( distortion) nd mkes rel, diminished nd inverted imge on the ilm CCD sensor, so ll o them must work s convexconcve lens (choose one) ocl length is bout the lens-ilm distnce when ocused t ininity depth o ield connected with the perture sensitivity o the ilm corresponds with the energy needed or the exposure, which is product o time nd perture long time + smll perture = big depth o ield everything shrp short time + big perture = smll depth o ield shrp imges o objects hving the sme object distnce L , , 128-9, 133 Answers: m, 0.33 m cm, 32.7 cm D (when = 1.6 cm) D, 0.5 D, -0.1 D GEOMETRICAL OPTICS