Welcome to: Physics I. I m Dr Alex Pettitt, and I ll be your guide!

Transcription

1 Welcome to: Physics I I m Dr Alex Pettitt, and I ll be your guide!

2 Physics I: x Mirrors and lenses Lecture 13:

3 Last lecture: Reflection & Refraction Reflection: Light ray hits surface Ray moves away from surface = 1 Refraction: Light ray hits surface Ray enters object and changes speed & direction. 1 2 n 1 sin 1 = n 2 sin 2

4 Mirages Mirages occur when the refractive index, changes with position (lowers as T rises). The ray travels in a curved path. n nlow nhigh e.g. A temperature difference produces a density difference. Causes n to vary. Water on the road on a hot day Brain assumes ray, i, is straight see a reflection of the car, v

5 Mirages Not reflection Refraction!

6 Last lecture review: A fish sits below the surface of the water at P. An observer at O sees the fish at: a) a greater depth than it is O b) the same depth c) a smaller depth than it is P

7 Last lecture review: A fish sits below the surface of the water at P. An observer at O sees the fish at: a) a greater depth than it is O b) the same depth c) a smaller depth than it is P P Rays emerging from water converge above fish

8 Last lecture review: A fish sits below the surface of the water at P. An observer at O sees the fish at: a) a greater depth than it is O b) the same depth c) a smaller depth than it is P

9 Last lecture review: A fish sits below the surface of the water at P. An observer at O sees the fish at: a) a greater depth than it is O b) the same depth c) a smaller depth than it is P P Rays emerging from water converge above fish

10 Mirages Light path over a hot road. Is the air s refractive index... (a) increase from left to right (b) increase from right to left (c) increase upwards (d) increase downwards

11 Mirages Light path over a hot road. Is the air s refractive index... (a) increase from left to right (b) increase from right to left (c) increase upwards (d) increase downwards Light is bending away from the normal n is higher at the top.

12 Mirages Light path over a hot road. The person sees a mirage that looks like water. It appears to be at: (a) point A (c) point C (b) point B (d) point D

13 Mirages Light path over a hot road. The person sees a mirage that looks like water. It appears to be at: (a) point A (c) point C (b) point B (d) point D

14 Optics Mirrors and lenses

15 Plane (flat) Mirrors Light from the triangle reflects off the mirror to the eye. Eye assumes light rays are straight Sees the triangle behind the mirror. Image is virtual : no light actually comes from behind the mirror.

16 Plane Mirrors Where is the image? Distance from mirror? Height?????

17 Plane Mirrors 2 light rays needed to locate each point in the mirror. locate arrow top locate arrow bottom congruent triangles (sides & angles equal) arrow to mirror distance = image to mirror distance Rays top and bottom of arrow are normal to mirror and parallel image is same height as arrow

18 Plane Mirrors Plane mirror image has same length and orientation (not upside down) as object. But reverse the object front-to-back. Your right hand looks like your left hand.

19 Curved Mirrors Parabolic curved mirror: If ray is parallel to axis, it will be reflected through the focal point/ focus. axis focal point angle with normal = angle with line to focal point Can concentrate light at the focal point or put light source at the focal point and get parallel rays

20 Curved Mirrors Parabolic curved mirror: If ray is parallel to axis, it will be reflected through the focal point/ focus. axis focal point angle with normal = angle with line to focal point Can concentrate light at the focal point or put light source at the focal point and get parallel rays

21 Curved Mirrors Close to apex, mirror looks spherical. Easier to make spherical mirrors axis focal point most focussing mirrors are spherical. slight image distortion: spherical aberration Famous example: Hubble Space Telescope Mirror made with wrong curve, big spherical aberration.

22 Curved Mirrors focal length To minimise spherical aberration: Mirror small fraction of whole sphere Focal length >> mirror Rays strike the mirror ~ parallel to axis paraxial approximation

23 Curved Mirrors To find image draw 2 rays from different points on the object. Any ray possible, but these are simplest: (1) A ray parallel to the mirror axis reflects through the focal point. (2) A ray passing through the focal point reflects parallel to the axis. (3) A ray striking the center of the mirror reflects symmetrically about the mirror axis. (4) A ray through the centre of curvature of the mirror returns on itself.

24 Curved Mirrors Examples: Locate image top with 2 rays (types 1 & 2) Light rays come from the image and converge as a real image From symmetry, bottom of image is on the axis. (also, ray along axis is reflected straight back, type 4)

25 Curved Mirrors Examples: move object closer to mirror Locate image top with 2 rays (types 1 & 2) From symmetry, bottom of image is on the axis. Light rays come from the image: real image As object gets closer to mirror, image size increases. When object is between mirror centre (C) and focus point (F), image is larger than object and further away.

26 Curved Mirrors What does a real image look like?

27 Curved Mirrors What does a real image look like?

28 Curved Mirrors Examples: move object closer to mirror Locate image top with 2 rays (types 1 & 2) From symmetry, bottom of image is on the axis. Rays diverge (go apart) after reflection. Appear to cross behind the mirror Light rays do not come from the image: virtual image Image is upright and enlarged.

29 Curved Mirrors

30 Curved Mirrors

31 Curved Mirrors Convex mirrors Reflected rays diverge Only forms virtual images Reflected parallel rays appear to come from the focal point behind the mirror, F Image is always upright (not inverted) and smaller. Used to image large area in small space (wide angle view)

32 Curved Mirrors Convex mirrors

33 Curved Mirrors Real vs virtual: Real image: rays converge. Actual photons travel the path, and are collected at I. You can project image onto a screen. Virtual image: rays diverge. No photons travel the path, light is dispersed. You cannot project image onto a screen.

34 Please see handout Q1

35 Mirror Equation Drawing rays works but can we be more accurate? 2 rays (type 1 & 3) Similar triangles: h s h 0 s 0 inverted image: negative h s and s both >0. (virtual image: negative s ) Here, M = h0 h = M < 1 s0 s (magnification) because image is smaller and negative, because image is inverted

36 Mirror Equation Drawing rays works but can we be more accurate? 2 rays (type 1 & 3) Similar triangles #2 : h 0 s 0 f f h h 0 h = (s0 f) f 1 s + 1 s 0 = 1 f M = h 0 /h = s 0 /s mirror equation s 0 s = (s0 f) f

37 Mirror Equation 1 s + 1 s 0 = 1 f If image is virtual: s 0 < 0 image distance is negative If mirror is convex: f<0

38 Mirror Equation Example The Hubble Space Telescope has a mirror with 5.52 m focal length. A man stands 3.85 m in front of the mirror. What is the (a) location (b) magnification of the image? mirror equation: 1 s + 1 s 0 = 1 f s 0 = s fs f = (5.52m)(3.85m) 3.85m 5.52m = 12.7m

39 Mirror Equation Example The Hubble Space Telescope has a mirror with 5.52 m focal length. A man stands 3.85 m in front of the mirror. What is the (a) location (b) magnification of the image? M = s0 s = 12.7m 3.85m =3.30

40 Please see handout Q2

41 Mirror Equation 1 s + 1 s 0 = 1 f Remember the point of C is at: 2f = R

42 Mirror Equation Example Jurassic Park OBJECTS IN MIRROR ARE CLOSER THAN THEY SEEM.

43 Mirror Equation Example If the mirror s curvature radius is 12 m and the T. rex is 9.0 m away, what is its magnification? 1 mirror equation: s + 1 s 0 = 1 s 0 = fs f s f M = = s0 s = fs/(s f) s ( 6.0m) 9.0m ( 6.0m) =0.4 = s f f and f = R/2 = 6.0m 40% of actual size, so seems to be further away.

44 Lenses

45 Lenses A lens uses refraction to form images. Converging lens Convex lens that focusses parallel rays to the focal point Diverging lens Concave lens: parallel rays seem to move away from a common focus. Only forms virtual images. Because lenses refract, not reflect, this is opposite to mirrors.

46 Lenses Thin lens approximation Thickness << curvature radius Although the ray refracts twice (as it enters lens and as it exits) thin lens single refraction Rays can pass through a lens in 2 directions Focal length is the same both sides.

47 Lenses Ray through lenses (1) Ray parallel to lens axis refracts through the focal point. (2) Ray passing through the centre travels straight. Use these two rays to find images formed with lenses.

48 Lenses Examples Object further than two focal lengths, s>2f Image smaller and inverted. Light rays come from the image: real image (do not need to look through lens to see images)

49 Lenses Examples: approach the lens Distance to image gets larger. Image becomes larger.

50 Lenses Examples: approach the lens Object closer than focal length, s<f Image large and virtual: rays do not come from image Can only be seen looking through the lens.

51 Lenses

52 Lenses Concave (diverging) lens always forms a smaller, upright image. Only visible through the lens.

53 The lens equation s h s -h Similar triangles: M = h0 h = s0 s Magnification (same as mirrors)

54 The lens equation h f Similar triangles #2: h 0 s 0 f = h f s 0 f -h 1 s + 1 s 0 = 1 f lens equation (same as mirror equation)

55 The lens equation

56 The lens equation Example You use a magnifying glass with a 30- cm focal length to read. How far from the page should you hold the lens to see the print enlarge 3 x? M = 1 s0 s =3 s 0 = 3s 1 1 s + 1 s 0 = 1 f s 3s = 2 3s = 1 f = 1 30cm s = (2)(30cm) 3 = 20cm

57 Please see handout Q3

58 Example 1: eyes Eye focuses light on the retina on the back of the eyeball. Lens can change shape to alter f. An extra lens can be used to correct problems with eyes: Nearsighted Farsighted

59 Example 2: micro/telescopes Used to enlarge images. First lens magnifies and flips the image. The second places a virtual image at a large distance so the eye can focus. Focus by changing L Telescopes similar, but the object is much further away! There are also reflecting telescopes. object at infinity focuses on f

60 Homework A bit of extra homework Equations are quite simple, so instead go and practice drawing ray tracing diagrams. Lots of cool interactive physics simulations here: simulations/category/physics