Spherical Mirrors. Types of spherical mirrors. Lecture convex mirror: the. geometrical center is on the. opposite side of the mirror as

Transcription

1 Lecture 14-1 Spherical Mirrors Types of spherical mirrors covex mirror: the geometrical ceter is o the opposite side of the mirror as the object. cocave mirror: the geometrical ceter is o the same side of the mirror as the object. A plae mirror ca be thought of as a spherical mirror of a ifiitely large radius of curvature r. Covex/cocave viewed from frot

2 Lecture 14-2 Focal Poit of a Spherical Mirror Whe parallel rays icidet upo a spherical mirror, the reflected rays or the extesios of the reflected rays all coverge toward a commo poit, the focal poit of the mirror. Distace f is the focal legth. why? Real focal poit: the poit to which the reflected rays themselves pass through. This is relevat for cocave mirrors. f Rays ca be traversed i reverse. Thus, rays which (would) pass through F ad strike the mirror will emerge parallel to the cetral axis.

3 Lecture 14-3 Covex Spherical Mirror Virtual focal poit: the poit to which the extesios of the reflected rays pass through. This is relevat for covex mirrors. Rays ca be traversed i reverse. Thus, rays which (would) pass through F ad strike the mirror will emerge parallel to the cetral axis. f The image is always virtual, reduced, has the same orietatio as the object ad closer behid the mirror. The field of view is, therefore, larger tha that of a plae mirror.

4 Lecture 14-4 Locatig Images oly usig the parallel, focal, ad/or radial rays. Real images form o the side of a mirror where the objects are, ad virtual images form o the opposite side.

5 Lecture 14-5 Physics 219 Questio 1 March 2, Oe of the followig ray diagrams below for a cocave spherical mirror is icorrect ad is impossible. Fid which oe. C stads for the ceter of curvature ad F stads for the focal poit.

6 Lecture 14-6 Derivig the Mirror Equatio ( < 0) OA IJ h h ' = = AC JC p R R q h' R q = h p R But h' JV q = = h AV p = p q R 1 f Trasverse magificatio m: m > 0 if image is upright, m < 0 if iverted. m = h /h = q/ p If p, the q=r/2. So we must have f=r/2.

7 Lecture 14-7 Sigs i Mirror Equatio ad Magificatio = p q f m y' = = y m q p q p (f = R/2) p is positive if the object is i frot of the mirror (real object) p is egative if it is i back of the mirror (virtual object) q is positive if the image is i frot of the mirror (real image) q is egative if it is i back of the mirror (virtual image) m is positive if image ad object have the same orietatio (upright) m is egative if they have opposite orietatio (iverted) f ad R are positive if ceter of curvature i frot of mirror (cocave) f ad R are egative if it is i back of the mirror (covex)

8 Lecture 14-8 Physics 219 Questio 2 March 2, A object of 1 cm height is 20 cm i frot of a cocave mirror of focal legth 15 cm. Pick the correct statemet about its image. A. Virtual, upright, 60 cm behid the mirror B. Virtual, iverted, 30 cm behid the mirror C. Real, upright, 45 cm i frot of the mirror D. Real, iverted, 60 cm i frot of the mirror E. Real, upright, 3 cm i height

9 Lecture 14-9 Geometric Optics Study of light (ad other EM waves) as they propagate i straight lies called rays. Light ca travel through matter medium as well as free space (vacuum). Iside matter, the speed of light v is geerally less tha c. (This speed ca eve c deped o wavelegth.) ( ) v < c, > 1 v idex of refractio Whe light ecouters a iterface betwee differet media, it ca geerally both reflect ad refract. Medium 1 Medium 2

10 Lecture Huyges s Priciple Each poit o a primary wavefrot serves as the source of spherical secodary wavelets that advace with a speed ad frequecy equal to those of the primary wave. The primary wavefrot at some later time is the evelope of these wavelets. t 1 t 2 t 3 wavelet poits of give phase t 1 t 2 t 3

11 Lecture Reflectio from Huyges s Priciple ΔABB '' ΔBAP θ = θ ' = ct

12 Lecture Refractio from Huyges s Priciple θ 1 = φ1 θ2 = 2 vt siφ = AB = φ vt siφ medium vacuum 1 air water 1.33 glass = v v v c/ = c/ i c 1 λ λi = = = f f i i idex of refractio Sell s Law where λ is the wavelegth i vacuum

13 Lecture Image by Refractio: What a Bird Sees (same d idepedet of s) = w i a t θ θ w i a t (small agles) ad taθ taθ w i a t w s s a a d' d d' w d

14 Lecture Refractio through Multiple Media θ 1 θ 2 θ 2 θ = = = Here, 1 < 2, 2 > 3, ad 1 > 3. Why? (The larger, the smaller the agle θ.) θ 1 θ 3 As i this example, if 1 = 3, the θ 1 = θ 3, or the icidet ad fial outgoig rays are parallel to each other.

15 Lecture Total Iteral Reflectio All light ca be reflected, oe refractig, whe light travels from a medium of higher to lower idices of refractio. medium 2 e.g., glass ( 1 =1.5) to air ( 2 =1.0) 2 1 > 1 = θ 2 > θ But θ caot be greater tha 90! medium 1 I geeral, if si θ 1 > ( 2 / 1 ), we have NO refracted ray; we have TOTAL INTERNAL REFLECTION. θ c 1 si 2/ 1 ( ) Critical agle above which this occurs.

16 Lecture Examples Fish s view of the world θ c = si Prism used as reflectors θ c = si (e.g., glass with =1.5) θ c Optical fiber θ c = si (e.g., core =1.5, claddig =1.5)