Understanding Optics and Human Vision Concepts

Recitations and labs • Recitations start this week – Wed first day • If you have not signed up yet please do so asap • Homework #1 due this week in recitation class • Labs start next week • An announcement from physlabs@pas.rochester.edu will be mailed soon. Lecture II

Lenses, mirrors and human eye Physics 123, Spring, 2006 Lecture II

Concepts • Concave and convex mirrors • Focus • Converging and diverging lenses • Lens equation • Eye as an optical instrument • Far and near points • Corrective lenses System of lenses Lecture II

Spherical mirrors • Convex mirror bulges out – diverges light • Concave mirror caves in – converges light Lecture II

Focus • Parallel beam of light (e.g. from a very distant object) is converged in 1 point – focal point F • Distance from the mirror to F is called focal distance, or focus f =r/2 Lecture II

Ray tracing 3 Easy rays: • Parallel  through focus • Through focus  parallel (reversible rays) • Through the center of curvature C  itself Lecture II

Magnification • h0 – object height • h0>0 - always • hi – image height • hi>0– upright image • hi<0– inverted image • m=hi/h0 - magnification |m|>1 –image larger than object |m|<1 –image smaller than object Lecture II

Mirror equation • d0 – distance to object • d0>0 - always • di – distance to image • di>0– real image • di<0– virtual image Lecture II

Convex mirror • Virtual focus – parallel beam focuses behind the mirror: f<0 • Same rules for ray tracing. Lecture II

Sign convention for mirrors • hi>0di<0 – upright image is always virtual • hi<0di>0 – inverted image is always real Lecture II

Concave mirror d0>r – (real, inverted), smaller r>d0>f – (real, inverted), larger d0<f – (virtual, upright), larger Convex mirror Image is always (virtual, upright), smaller. Images in curved mirrors Lecture II

Lenses • Convex lens bulges out –converges light • Concave lens caves in –diverges light Lecture II

Focus • Light goes through – focal points on both sides – F and F’ • Always a question which focal point to choose when ray tracing • Converging lens: • Parallel beam of light is converged in 1 point – focal point F • Real focus: f>0 • Key for the focal point choice: Rays must bend in • Diverging lens: • Parallel beam of light seems to be coming out of 1 point F • Virtual focus: f<0 • Key for the focal point choice: Rays must bend out Lecture II

Ray tracing for converging lens • 3 Easy rays: • Parallel  through focus F • Through focus F’ parallel (reversible rays) • Through the center  itself Lecture II

Diverging lens • Same rules, but remember to diverge (bend out) • Parallel  projection through focus F • Projection through F’  parallel • Through the center  goes through Lecture II

Lens equation • d0 – distance to object • di – distance to image • f –focus • P – power of lens, in Dioptry (D=1/m) • f must be in m Lecture II

Sign convention for lenses and mirrors • hi>0di<0 – upright image is always virtual • hi<0di>0 – inverted image is always real Lecture II

Converging lens, concave mirror d0>2f – (real, inverted), smaller 2f>d0>f – (real, inverted), larger d0<f – (virtual, upright), larger Diverging lens, convex mirror Image is always (virtual, upright), smaller. Images in lenses and mirrors Lecture II

System of lenses • Image of the 1st lens of object for the 2nd lens. Lecture II

Eye as an optical instrument • Eye is a converging lens • Ciliary muscles are used to adjust the focal distance. • f is variable • Image is projected on retina – back plane. • di stays constant • Image is real (light excites the nerve endings on retina)  inverted (we see things upside-down) • di>0, hi<0 • Optic nerves send ~30 images per second to brain for analysis. Lecture II

Far and near points for normal eye • Relaxed normal eye is focused on objects at infinity – far point f0=eye diameter =~2.0 cm • Near point – the closest distance at which the eye can focus - for normal eye is ~25cm. Adjusted focus: f1=1.85 cm Lecture II

Corrective lenses • Nearsighted eye • far point<infinity • diverging lens f<0  P<0 • Farsighted eye • near point > 25 cm • converging lens f>0  P>0 • Lens+eye = system of lenses • Corrective lenses create virtual, upright image (di<0 !) at the point where the eye can comfortably see • Farsighted eye • Near point = 70 cm  di =-0.70m • Need to correct near point • Object at “normal near point” =25cm • Nearsighted eye • Far point = 17 cm  di =-0.17m • Need to correct far point • Object at “normal far point” =infinity Lecture II

Converging lens - for farsighted d0>2f – (real, inverted), smaller 2f>d0>f – (real, inverted), larger d0<f – (virtual, upright), larger Diverging lens - for nearsighted Image is always (virtual, upright), smaller. Images in lenses Image in corrective lenses is always virtual and upright di<0 and hi>0 Lecture II

Corrective lenses • Nearsighted eye • Far point = 17cm • Near point = 12 cm • P-? • new near point -? • Diverging lens projects infinity to 17 cm from the eye Lecture II

Real and virtual image O I M Mirrors: I and O – same side I and O – opposite sides Real, inverted light goes through Virtual, upright light does not go through O M I Lenses: I and O – opposite sides I and O – same side Real, inverted light goes through O L I Virtual, upright light does not go through O I L Lecture II

Understanding Optics and Human Vision Concepts