Lenses, Mirrors & the Human Eye

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

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

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

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

LENS QUESTIONS LENS APPLET

Image formed by a diverging lens ) Object between F and lens                                           Virtual Erect Larger than object Behind the object on the same side of the lens Image formed by a diverging lens e) Object at F Characteristics of the image regardless of object postion Virtual Erect Smaller than object Between object and lens

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

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

Sign convention for lenses and mirrors h0>0 di>0 – real image Opposite side from O di<0 - virtual image Same side with O hi>0 – upright image hi<0 - inverted image f>0 – concave mirror f<0 – convex mirror f>0 – converging lens f<0 – diverging lens hi>0di<0 – upright image is always virtual hi<0di>0 – inverted image is always real

Images in lenses and mirrors 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.

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

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

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

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

Magnification h0 – object height hi – image 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

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

Convex mirror Virtual focus – parallel beam focuses behind the mirror: Same rules for ray tracing.

Sign convention for mirrors d0>0 h0>0 di>0 – real image di<0 - virtual image hi>0 – upright image hi<0 - inverted image f>0 – concave mirror f<0 – convex mirror hi>0di<0 – upright image is always virtual hi<0di>0 – inverted image is always real

Images in curved mirrors 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.

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.

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

Corrective lenses Farsighted eye Nearsighted eye 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

Images in lenses 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. Image in corrective lenses is always virtual and upright di<0 and hi>0

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

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