VIEWS: 2 PAGES: 60 POSTED ON: 8/26/2011
Property 5: Refraction experiment ? particle (photon)? wave (E&M) ? Property 5: Refraction • experiment: objects in water seem closer than they really are when viewed from air eye air water apparent location real object Property 5: Refraction • particle (photon) ? incident ray air surface water refracted ray Property 5: Refraction • particle (photon) ? incident ray vxair = vxwater vxair air vyair vyair < vywater surface therefore water vxwater vi < vr vywater refracted ray Property 5: Refraction normal line • wave (E&M) ? incident wave air surface surfac e water refracted wave normal line Property 5: Refraction crest of following wave • wave (E&M) ? crest of wave incident wave air crest of preceding wave air air surface x water water refracted wave normal line Property 5: Refraction • particle (photon) theory: vwater > vair • wave (E&M) theory: vwater < vair • experiment ? Property 5: Refraction • particle (photon) theory: vwater > vair • wave (E&M) theory: vwater < vair • experiment: vwater < vair wave theory works! particle theory fails! Properties 1, 2 & 5 Speed, Color and Refraction • Speed of light changes in different materials • Speed is related to frequency and wavelength: v = f • If speed changes, does wavelength change, frequency change, or BOTH? Properties 1, 2 & 5 • Speed, Color and Refraction • Speed of light changes in different materials • Speed is related to frequency and wavelength: v = f • What changes with speed? – Frequency remains constant regardless of speed – Wavelength changes with speed Refraction and Thin Lenses Can use refraction to try to control rays of light to go where we want them to go. Let’s see if we can FOCUS light. Refraction and Thin Lenses What kind of shape do we need to focus light from a point source to a point? lens with some shape for front & back point source of light screen s’ = image distance s = object distance Refraction and Thin Lenses Let’s try a simple (easy to make) shape: SPHERICAL. Play with the lens that is handed out Does it act like a magnifying glass? Refraction and Thin Lenses Let’s try a simple (easy to make) shape: SPHERICAL. Play with the lens that is handed out Does it act like a magnifying glass? Does it focus light from the night light? Refraction and Thin Lenses Let’s try a simple (easy to make) shape: SPHERICAL Play with the lens that is handed out Does it act like a magnifying glass? Does it focus light from the night light? Does the image distance depend on the shape of the lens? (trade with your neighbor to get a different shaped lens) Refraction and Thin Lenses Spherical shape is specified by a radius. The smaller the sphere (smaller the radius), the more curved is the surface! R R R1 R2 Refraction and the Lens-users Eq. f>0 1 1 1 s > 0 AND s > f = + f s s' s’ > 0 AND s’ > f f f s s’ Example: f = 10 cm; s = 20 cm; s’ = 20 cm: 1/20 + 1/20 = 1/10 Refraction and the Lens-users Eq. 1 1 1 as s gets bigger, = + f s s' s’ gets smaller f f s s’ Example: f = 10 cm; s = 40 cm; s’ = 13.3 cm: 1/40 + 1/13.3 = 1/10 Refraction and the Lens-users Eq. 1 1 1 as s approaches infinity = + f s s' s’ approaches f f f s s’ Example: f = 10 cm; s = 100 cm; s’ = 11.1 cm: 1/100 + 1/11.1 = 1/10 Refraction and the Lens-users Eq. f>0 1 1 1 s > 0 AND s > f = + f s s' s’ > 0 AND s’ > f f f s s’ Example: f = 10 cm; s = 20 cm; s’ = 20 cm: 1/20 + 1/20 = 1/10 Refraction and the Lens-users Eq. 1 1 1 = + as s gets smaller, f s s' s’ gets larger f f s s’ Example: f = 10 cm; s = 13.3 cm; s’ = 40 cm: 1/13.3 + 1/40 = 1/10 Refraction and the Lens-users Eq. 1 1 1 = + as s approaches f, f s s' s’ approaches infinity f f s s’ Example: f = 10 cm; s = 11.1 cm; s’ = 100 cm: 1/11.1 + 1/100 = 1/10 Refraction and the Lens-users Eq. Before we see what happens when s gets smaller than f, let’s use what we already know to see how the lens will work. Refraction and the Lens-users Eq. – Any ray that goes through the focal point on its way to the lens, will come out parallel to the optical axis. (ray 1) f f ray 1 Refraction and the Lens-users Eq. – Any ray that goes through the focal point on its way from the lens, must go into the lens parallel to the optical axis. (ray 2) f f ray 1 ray 2 Refraction and the Lens-users Eq. – Any ray that goes through the center of the lens must go essentially undeflected. (ray 3) object image f ray f 1 ray 3 ray 2 Refraction and the Lens-users Eq. – Note that a real image is formed. – Note that the image is up-side-down. object image f ray f 1 ray 3 ray 2 Refraction and the Lens-users Eq. – By looking at ray 3 alone, we can see by similar triangles that M = h’/h = -s’/s. object h s image ’ f h’<0 s f ray 3 Example: f = 10 cm; s = 40 cm; s’ = 13.3 cm: note h’ is up-side-down and so is <0 M = -13.3/40 = -0.33 X Refraction and the Lens-users Eq. This is the situation when the lens is used in a camera or a projector. Image is REAL. object image f ray f 1 ray 3 ray 2 Refraction and the Lens-users Eq. What happens when the object distance, s, changes? object image f ray f 1 ray 3 ray 2 Refraction and the Lens-users Eq. Notice that as s gets bigger, s’ gets closer to f and |h’| gets smaller. object image f ray f 1 ray 3 Example: f = 10 cm; s = 100 cm; s’ = 11.1 cm: M = -11.1/100 = -0.11 X ray 2 Focusing To focus a camera, we need to change s’ as s changes. To focus a projector, we need to change s as s’ changes. We do this by screwing the lens closer or further from the film or slide. But what about the eye? How do we focus on objects that are close and then further away with our eyes? Do we screw our eyes in and out like the lens on a camera or projector? Focusing But what about the eye? How do we focus on objects that are close and then further away with our eyes? Do we screw our eyes in and out like the lens on a camera or projector? - NO, instead our eyes CHANGE SHAPE and hence change f as s changes, keeping s’ the same! Refraction and the Lens-users Eq. Let’s now look at the situation where s < f (but s is still positive): s f f Refraction and the Lens-users Eq. We can still use our three rays. Ray one goes through the focal point on the left side. ray 1 s f f Refraction and the Lens-users Eq. Ray two goes through the focal point on the right side (and parallel to the axis on the left). ray 1 s f f ray 2 Refraction and the Lens-users Eq. Ray three goes through the center of the lens essentially undeflected. ray 1 h’ s f f s’ ray 2 ray 3 Refraction and the Lens-users Eq. Notice that: s’ is on the “wrong” side, which means that s’ < 0 , and that |s’| > |s| so f > 0. ray 1 h’ s f f s’ ray 2 ray 3 Example: f = 10 cm; s = 7.14 cm; s’ = -25 cm: 1/7.14 + 1/(-25) = 1/10 Refraction and the Lens-users Eq. Notice that: h’ right-side-up and so h’ > 0., M = h’/h = -s’/s . M > 0 (s’ < 0 but -s’ > 0). h’ s f f s’ ray 3 Example: f = 10 cm; s = 7.14 cm; s’ = -25 cm: M = - (-25)/ 7.14 = 3.5 X Refraction and the Lens-users Eq. This is the situation when the lens is used as a magnifying glass! Image is VIRTUAL. ray 1 h’ s f f s’ ray 2 ray 3 Refraction and the Lens-users Eq. The same lens can be used as: • a camera lens: s >> f, s > s’, M < 0, |M| < 1 • a projector lens: s > f, s’ > s, M < 0, |M| > 1 • a magnifying glass: s < f, s’ < 0, M > 0, M > 1 Refraction and the Lens-users Eq. Notes on using a lens as a magnifying glass: • hold lens very near your eye • want IMAGE at best viewing distance which has the nominal value of 25 cm so that s’ = -25 cm. Refraction and the Lens-users Eq. Are there any limits to the magnifying power we can get from a magnifying glass? Refraction and the Lens-users Eq. • Magnifying glass has limits due to size • As we will see in a little bit, magnifying glass has limits due to resolving ability • NEED MICROSCOPE (two lens system) for near and small things; need TELESCOPE (two lens system) for far away things. Telescope Basics Light from far away is almost parallel. objective lens eyepiece fe fo Telescope Basics: Get More Light The telescope collects and concentrates light. objective lens eyepiece fe fo Telescope Basics Light coming in at an angle, in is magnified to out . objective lens eyepiece x fo fe Magnification in = x/fo, out = x/fe; M = out/in = fo/fe objective lens eyepiece x fo fe Limits on Resolution telescopes – magnification: M = out/in = fo /fe – light gathering: Amt D2 – resolution: 1.22 = D sin(limit) so in = limit and out = 5 arc minutes so limit 1/D implies Museful = 60/in * D where D is in inches – surface must be smooth on order of Limits on Resolution: calculation Mmax useful = out/in = eye/limit = 5 arc min / (1.22 * / D) radians = (5/60)*(/180) / (1.22 * 5.5 x 10-7 m / D) = (2167 / m) * D * (1 m / 100 cm) * (2.54 cm / 1 in) = (55 / in) * D Example What diameter telescope would you need to read letters the size of license plate numbers from a spy satellite? Example • need to resolve an “x” size of about 1 cm • “s” is on order of 100 miles or 150 km • limit then must be (in radians) = 1 cm / 150 km = 7 x 10-8 • limit = 1.22 x 5.5 x 10-7 m / D = 7 x 10-8 so D = 10 m (Hubble has a 2.4 m diameter) Limits on Resolution: further examples • other types of light – x-ray diffraction (use atoms as slits) – IR – radio & microwave • surface must be smooth on order of Review of Telescope Properties 1. Magnification: M = fo/fe depends on the focal lengths of the two lenses. 2. Light gathering ability: depends on area of objective lens, so depends on diameter of objective lens squared (D2). 3. Resolution ability: depends on diameter of objective lens: Max magnification = 60 power/in * D. Types of Telescopes The type of telescope we have looked at so far, and the type we have or will have made in the lab is called a refracting telescope, since it uses the refraction of light going from air to glass and back to air. This is the type used by Galileo. There is a second type of telescope invented by Newton. It is called the reflecting telescope since it uses a curved mirror instead of a curved lens for the objective. There are three main sub-types of reflectors that we’ll consider: Prime focus, Newtonian, and Cassegranian. Refracting Telescope Two lenses (as we had in the lab) objective lens eyepiece fe fo Reflecting Telescope Light from far away mirror focuses light problem: how do we get to focused light without blocking incoming light? Reflecting Telescope Prime Focus Light from far away mirror focues eyepiece light Solution #1: If mirror is big enough (say 100 to 200 inches in diameter), we can sit right in the middle and we won’t block much light - this is called the prime focus. Reflecting Telescope Newtonian Focus Light from far away eyepiece primary mirror focuses mirror light Solution #2: Use secondary mirror to reflect light out the side of the telescope- this is called the Newtonian focus. Reflecting Telescope Cassegranian Focus Light from far away primary mirror focuses light mirror eyepiece Solution #3: Use secondary mirror to reflect light out the back of the telescope- this is called the Cassegranian focus.