Transcript Heat Flow
Geometrical Optics and Mirrors • • • • • • • • • Geometrical Optics Reflection Plane Mirrors Spherical Mirrors Focal Length Ray Tracing Example – real image Example – inverted image Sign Rule and Summary Geometrical Optics • Formation of Image – Light reflected from object. – Some paths enter eye. • Geometrical Optics – Reflected light follows straight line paths (Rays) – Following path of these rays defines image we see Reflection • Reflection – Reflected paths manipulated by mirrors – Paths focused to form images • Reflection rules – Angle of incidence = angle of reflection – Specular vs diffuse reflection Plane Mirror • Scattered light follows path A-B-eye, but appears to be coming from C-B-eye. • Object and image distance • Angle incidence = angle reflection • Virtual vs. real image How Tall is the mirror? • Person want to see entire self in mirror – 1.5 m to eye level – 1.6 m to top of head • Ray coming off shoe, top of head – Bottom edge of mirror 0.75 m from floor – Top edge of mirror 1.55 m from floor – 0.8 m high Microwave Mirror – Shuttle Tile Fault Detection • Test panel of 12 tiles on aluminum backplate. • Interrogate by microwave horns at 45° angle, raster x-y direction. • Preliminary test – need smaller horns. www.msi-sensing.com Spherical and Parabolic Mirrors • Focusing light rays at a point – Light originates from infinity, reflects to focal point – Principal axis, focus, focal length – Spherical aberration, circular vs. parabolic mirror Spherical Mirror for small angles • Examine ray coming from infinity – Radius from C normal to mirror – All angles θ equal – BCF is isosceles triangle (BF = CF) – For small θ BF=AF and 𝒇 = 𝒓 𝟐 Image formation – Ray diagrams • Tracing principle rays – – – – Place arrow principal axis Tail reflects on itself Trace principal rays of tip Everything else falls between • Principal rays 1. 2. 3. 4. Comes parallel to axis, reflects through focal point. Goes through focal point, emerges parallel to axis. Hits mirror at normal incidence, reflects back on itself. All converge at I’ Mirror equation • Two similar triangles ℎ𝑜 ℎ𝑖 = 𝑑𝑜 𝑑𝑖 ℎ𝑜 ℎ𝑖 = 𝑂𝐹 𝐹𝐴 1 𝑑𝑜 + 1 𝑑𝑖 = 𝑑𝑜 −𝑓 𝑓 • Combining 𝑑𝑜 𝑑𝑖 = 𝑑𝑜 −𝑓 𝑓 = 1 𝑓 𝑚= ℎ𝑖 ℎ𝑜 =− 𝑑𝑖 𝑑𝑜 Two sets of similar triangles Example – Concave Mirror • A 1.5 cm high diamond ring is placed 20 cm from a concave mirror with radius of curvature 30 cm. Determine – (a) the position of the image and di = 60 cm – (b) its size m = -60/20 = -3 – hi = -3 ho = -4.5 cm – Inverted – “Real” image 1 𝑑𝑜 1 1 +𝑑 =𝑓 𝑖 𝑑 𝑚 = − 𝑑𝑖 𝑜 Example – Object closer than focal length • A 1.5 cm high object is place 10 cm from a concave mirror whose radius of curvature is 30 cm. (a) Draw a principal ray diagram and the position of the image (b) determine the position of the image and (c) the magnification – di = -30 cm – m = --30/20 = +3 – hi = +3 ho = +4.5 cm – Upright, virtual 1 𝑑𝑜 + 1 𝑑𝑖 = 1 𝑓 𝑚=− 𝑑𝑖 𝑑𝑜 Summary Convex rear-view mirror An external rearview car mirror is convex with a radius of curvature 16 m. Determine the location of the image and its magnification for an object 10 m from the mirror f = -8 m di= -4.4m m = - di/do = -- 4.4/10 = +0.44 1 1 1 + = 𝑑𝑜 𝑑𝑖 𝑓 𝑚=− 𝑑𝑖 𝑑𝑜