Last lecture: finishing up Chapter 22

Transcription

1 Last lectre: finishing p Chapter 22 Hygens principle consider each point on a wavefront to be sorce of secondary spherical wavelets that propagate at the speed of the wave at a later time t, new wavefront is the tangent to all of the secondary wavelets

2 A nice laboratory for Hygens principle

3 Index of refraction depends on wavelength Dispersion

4 How rainbows form water droplet

5 Geometric optics: mirrors and lenses Look at images formed when light waves fall on mirrors and lenses reflection and refraction taking place Contine to have sitations where light travels in straight lines geometric optics applies deal with rays to indicate the direction of travel of light Example: the plane mirror Consider image formed in a plane mirror

6 Plane mirror Label p the object distance Look at rays coming from object Rays diverge when reflecting off of the mirror, bt appear to originate from a point behind the mirror Point I is called the image of the object and q is called the image distance Lots of definitions in this chapter Images are formed at the point where the rays of light intersect, OR appear to originate If the rays of light actally pass throgh the image point, the image is real; if they only appear to originate from that point, the image is virtal

7 Ray tracing To find ot where an image is formed, have to follow at least two rays of light Consider the two rays coming from the object P as they reflect off of the mirror Trace the two reflected rays back to where they appear to originate from (behind the mirror) Triangles PQR and P QR are identical, which means that p=q image distance = object distance the image is as far behind the mirror as the object is in front of it Also, h=h ; the image size eqals the object size

8 Plane mirror Define lateral magnification M M= image height = h object height h For plane mirrors object is as far behind the mirror as object is in front image is nmagnified (M=1), virtal (not physically there) and pright bt there is a left-right reversal in the mirror

9 Where does the rock appear? For observer 1, it s at C What abot for observer 2?

10 Where does the rock appear? For observer 1, it s at C What abot for observer 2? C

11 How big does a fll-length mirror have to be? in order to be able to see yor entire body Mirror mst be half of the height of the man in order for him to see his fll reflection Fig. 23.4, p.716

12 Another qestion yo ve always wondered abot How does the day/night setting work in a car s rear-view mirror? Incident light refracts into glass, reflects off back srface and then refracts into eye Only small amont of light reflected from front srface makes it into eye

13 Spherical mirrors Spherical mirror has the shape of a segment of a sphere can be either concave, as mirror on right, or convex radis of crvatre is R; center of crvatre is C line drawn from C to V is called the principal axis

14 Spherical mirrors Consider a point sorce of light placed at position O Draw rays otward from O and look at rays reflected from mirror srface Rays converge to meet at location I I is called the image point; a real image is formed there, i.e. it actally exists We ll assme that the angles involved are small; for larger angles have to worry abot spherical aberration

15 Image from a spherical mirror Use ray tracing ray throgh C reflects back on itself ray throgh V reflects at angle q Image forms at I tan q = h/p tan q = -h /q With a magnification M = -h /h =-q/p More geometry tan a = h/(p-r) tan a = -h /(R-q) h /h = -(R-q)/(p-R) (R-q)/(p-R)=q/p after some algebra 1/p + 1/q = 2/R mirror eqation

16 Image has a magnification less than 1, is real and is inverted Spherical mirror

17 Rays from infinity Consider rays coming in from infinity (the object is very far away) The rays are parallel to the optical axis After reflection, they converge on point F 1/p + 1/q = 2/R If p=infinity, q=r/2=the focal length f So we can rewrite the mirror eqation as 1/p + 1/q = 1/f

18 Example

19 A spherical convex mirror Again, we do the raytracing thing Note that the rays appear to diverge from a point behind the mirror So it s a virtal (and pright) image being formed Mirror eqation still applies

20 Definitions

21 More definitions

22 Ray diagrams It s convenient to draw 3 particlar rays to determine the position and magnitde of an image Ray 1 is drawn parallel to the principal axis and is reflected back throgh the focal point F Ray 2 is drawn throgh the focal point. Ths, it is reflected parallel to the principal axis Ray 3 is drawn throgh the center of crvatre C and is reflected back on itself

23 Case 1 Object is otside center of crvatre of concave mirror Image is real, redced and inverted p is +; q is + (and smaller than p) m = -q/p is negative and <1

24 Case 2 Object is inside focal point of concave mirror Image is virtal, pright and magnified. a shaving or makep mirror

25 Case 3 Object is in front of convex mirror Image is virtal, pright and redced in size a sideview mirror