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Lenses, Mirrors & the Human Eye
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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
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Lenses Convex lens bulges out –converges light
Concave lens caves in –diverges light
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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
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Ray tracing for converging lens
3 Easy rays: Parallel through focus F Through focus F’ parallel (reversible rays) Through the center itself
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LENS QUESTIONS LENS APPLET
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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
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Diverging lens Same rules, but remember to diverge (bend out)
Parallel projection through focus F Projection through F’ parallel Through the center goes through
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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
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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>0di<0 – upright image is always virtual hi<0di>0 – inverted image is always real
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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.
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System of lenses Image of the 1st lens of object for the 2nd lens.
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Spherical mirrors Convex mirror bulges out – diverges light
Concave mirror caves in – converges light
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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
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Ray tracing 3 Easy rays: Parallel through focus
Through focus parallel (reversible rays) Through the center of curvature C itself
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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
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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
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Convex mirror Virtual focus – parallel beam focuses behind the mirror:
Same rules for ray tracing.
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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>0di<0 – upright image is always virtual hi<0di>0 – inverted image is always real
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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.
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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.
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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
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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
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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
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Corrective lenses Nearsighted eye Far point = 17cm Near point = 12 cm
new near point -? Diverging lens projects infinity to 17 cm from the eye
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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
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