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Lenses, Mirrors & the Human Eye Concepts Concave and convex mirrors –Focus Converging and diverging lenses –Lens equation Eye as an optical instrument.

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Presentation on theme: "Lenses, Mirrors & the Human Eye Concepts Concave and convex mirrors –Focus Converging and diverging lenses –Lens equation Eye as an optical instrument."— Presentation transcript:

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2 Lenses, Mirrors & the Human Eye

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

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

5 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

6 Ray tracing for converging lens 3 Easy rays: 1.Parallel  through focus F 2.Through focus F’  parallel (reversible rays) 3.Through the center  itself

7 LENS QUESTIONS LENS APPLET

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10 ) 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

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

12 Lens equation d 0 – distance to object d i – distance to image f –focus P – power of lens, in Dioptry (D=1/m) f must be in m

13 Sign convention for lenses and mirrors d 0 >0 h 0 >0 d i >0 – real image Opposite side from O d i <0 - virtual image Same side with O h i >0 – upright imageh i <0 - inverted image f>0 – concave mirrorf<0 – convex mirror f>0 – converging lensf<0 – diverging lens h i >0  d i <0 – upright image is always virtual h i 0 – inverted image is always real

14 Converging lens, concave mirror d 0 >2f – (real, inverted), smaller 2f>d 0 >f – (real, inverted), larger d 0

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

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

17 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

18 Ray tracing 3 Easy rays: 1.Parallel  through focus 2.Through focus  parallel (reversible rays) 3.Through the center of curvature C  itself

19 Magnification h 0 – object height –h 0 >0 - always h i – image height –h i >0 – upright image –h i <0 – inverted image m=h i /h 0 - magnification |m|>1 –image larger than object |m|<1 –image smaller than object

20 Mirror equation d 0 – distance to object –d 0 >0 - always d i – distance to image –d i >0 – real image –d i <0 – virtual image

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

22 Sign convention for mirrors d 0 >0 h 0 >0 d i >0 – real imaged i <0 - virtual image h i >0 – upright imageh i <0 - inverted image f>0 – concave mirrorf<0 – convex mirror h i >0  d i <0 – upright image is always virtual h i 0 – inverted image is always real

23 Images in curved mirrors Concave mirror d 0 >r – (real, inverted), smaller r>d 0 >f – (real, inverted), larger d 0

24 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. –d i stays constant Image is real (light excites the nerve endings on retina)  inverted (we see things upside-down) –d i >0, h i <0 Optic nerves send ~30 images per second to brain for analysis.

25 Far and near points for normal eye Relaxed normal eye is focused on objects at infinity – far point f 0 =eye diameter =~2.0 cm Near point – the closest distance at which the eye can focus - for normal eye is ~25cm. Adjusted focus: f 1 =1.85 cm

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

27 Converging lens - for farsighted d 0 >2f – (real, inverted), smaller 2f>d 0 >f – (real, inverted), larger d 0

28 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

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


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