32 Optical Imagesimage formationreflection & refractionmirror & lens equationsHuman eyeSpherical aberrationChromatic aberration
image formationreal image: rays converge to a point Ex. suns rays focused by magnifier virtual image: apparent source of light divergence Ex. image seen in mirror
Plane Mirror Imagedistances measured from mirror & axisimage height hi = object height hoobject distance do = image distance di
*concave mirror images
*convex mirror imagesalways virtual, upright, diminished
*Lens & Mirror Equationrelate do, di & f.lateral magnification (LM) = hi/ho.you must learn the sign conventions to use these formulas
imbedded objectimage distance < object distance
*lens powerpower = 1/(focal-length(meters))unit: [D, diopters, 1/m]used for corrective lenses
Ex. near-sighted person P = -5.0D f = 1/P = 1/(-5) = -0.2m = -20cm.
human eyeaverage index of refraction ~ 1.4
Far Sighted Eyecorrection requires converging lens
near sighted eyecorrection requires diverging lens
Spherical AberrationSpherical aberration: light striking near edge focus at different points than light striking near center
ChromaticAberrationChromatic aberration: different colors focus at different points
SummaryImage formation by lenses & mirrorsReal/virtual, orientation, magnification.Near & far-sighted problem & correctionSpherical & chromatic aberration
2. A document is sealed in a glass cube (n=1.5) at a depth of 10cm from one surface. Calculate s and m. Object is in n1=1.5. Viewer is in air n2=1.00. Radius of surface is r = infinity.
1/s = -0.15 s = -6.67cm.
Question: Reverse the designations in the example above. Object is now the fish, so n1 = 1.33 (fish location). Let the fish be 10cm from bowl surface. Where is the image of the fish formed that the cat will see?Answer: s = 10cm , s = ?, r = -15cm, n1 = 1.33, n2 = 1.00.
0.133 + 1/s = 0.022 1/s = -0.111 s = -9.00cm
Calculating Focal Length for a Thin LensExample: A double convex, thin glass lens with n = 1.5 has radii of curvature of 10 and 15cm. Find its focal length.
s, cats nosen1 holds object, here equal to 1.000.1 +1.33/s= 0.022 1.33/s = -0.078 s = -17.1cm