Transcript Chapter 35.
Ch. 35 Warmup22 Reflection •What happens when our wave hits a conductor? •E-field vanishes in a conductor Ei E0 sin kx t •Let’s say the conductor is at x = 0 •Add a reflected wave going other direction Er E0 sin kx t •In reality, all of this is occurring in three dimensions Incident Wave Reflected Wave Total Wave Warmup22 Law of Reflection ki = kr i = r •We assume the mirror is infinitely large •If the wavelength is sufficiently tiny compared to objects, this might be a good approximation i r •For the next week, we will always make this approximation Mirror •It’s called geometric optics •In geometric optics, light waves are represented by rays •You can think of light as if it is made of little particles •In fact, waves and particles act very similarly •First hint of quantum mechanics! Ans d Concept Question •This works for any angle •In 3D, you need three mirrors = 47 47 43 47 47 4343 Mirror Mirror A light ray starts from a wall at an angle of 47 compared to the wall. It then strikes two mirrors at right angles compared to each other. At what angle does it hit the wall again? A) 43 B) 45 C) 47 D) 49 E) 51 The Speed of Light in Materials •The speed of light in vacuum c is the same for all wavelengths of light, no matter the source or other nature of light c 3.00 108 m/s •Inside materials, however, the speed of light can be different •Materials contain atoms, made of nuclei and electrons •The electric field from EM waves push on the electrons •The electrons must move in response Indices of Refraction •Absorption and scattering Air (STP) 1.0003 •This generally slows the wave down Water 1.333 •n is called the index of refraction Ethyl alcohol 1.361 •The amount of slowdown can depend Glycerin 1.473 on the frequency of the light Fused Quartz 1.434 c v n Glass 1.5 -ish Cubic zirconia 2.20 Diamond 2.419 Warmup22 Refraction: Snell’s Law ck n •The relationship between the angular frequency and the wave number k changes inside a medium •Now imagine light moving from one medium to another f c n •Some light will be reflected, but usually most is refracted •The reflected light again must obey the law of reflection 1 = r k1sin1 n1 sin 1 n2 sin 2 index n1 1 r index n2 Snell’s Law y x 2 k2sin2 Snell’s Law: Illustration A light ray in air enters a region at an angle of 34. After going through a layer of glass, diamond, water, and glass, and back to air, what angle will it be at? A) 34 B) Less than 34 C) More than 34 D) This is too hard n5 = 1.5 6 n6 = 1 5 5 n3 = 2.4 n4 = 1.33 4 4 n1 = 1 n2 = 1.5 3 3 2 2 34 n1 sin 34 n2 sin 2 n3 sin 3 n4 sin 4 n5 sin 5 n6 sin 6 n1 sin 1 n2 sin 2 1 sin 34 1 sin 6 6 34 Ex - (From MCAT practice book). If a ray is refracted from air into a medium with n = 1.47 at an angle of incidence of 50, the angle of refraction is A. 0.059 B. 0.087 C. 0.128 D. 0.243 Ans A Image Formation Reflection Refraction I O CT-1- A fish swims below the surface of the water at P. An observer at O sees the fish at A. a greater depth than it really is. B. the same depth. C. a smaller depth than it really is. Ans C CT –2 A fish swims below the surface of the water. Suppose an observer is looking at the fish from point O'—straight above the fish. The observer sees Ans C the fish at A. a greater depth than it really is. B. the same depth. C. a smaller depth than it really is. Ex- (Serway 35-27) An opaque cylindrical tank with an open top has a diameter of 3.00 m and is completely filled with water. When the setting Sun reaches an angle of 28.0° above the horizon, sunlight ceases to illuminate any part of the bottom of the tank. How deep is the tank? Solve on Board Ex- (Serway 35-22) When the light illustrated below passes through the glass block, it is shifted laterally by the distance d. If n = 1.50, what is the value of d? Solve on Board Warmup23 Warmup23 Dispersion •The speed of light in a material can depend on frequency •Index of refraction n depends on frequency • Its dependence is often given as a function of wavelength in vacuum •Called dispersion •This means that different types of light bend by different amounts in any given material •For most materials, the index of refraction is higher for short wavelength Red Refracts Rotten Blue Bends Best Prisms •Put a combination of many wavelengths (white light) into a triangular dispersive medium (like glass) •Prisms are rarely used in research •Diffraction gratings work better •Lenses are a lot like prisms •They focus colors unevenly •Blurring called chromatic dispersion •High quality cameras use a combination of lenses to cancel this effect Rainbows •A similar phenomenon occurs when light bounces off of the inside of a spherical rain drop •This causes rainbows •If it bounces twice, you can get a double rainbow http://www.globalgiving.org/double-rainbow/ JIT Ans C Warmup23 Total Internal Reflection A trick question: A light ray in diamond enters an air gap at an angle of 60, then returns to diamond. What angle will it be going at when it leaves out the bottom? A) 60 B) Less than 60 C) More than 60 D) None of the above n1 = 2.4 60 2 2 n2 = 1 3 n3 = 2.4 n1 sin 60 n2 sin 2 sin 2 2.4 0.866 2.07 •This is impossible! •Light never makes it into region 2! •It is totally reflected inside region 1 •This can only happen if you go from a high index to a low •Critical angle such that this occurs: n2 sin c •Set sin2 = 1 n 1 View from the pool Which diver is more likely to see the lifeguard (Do as clicker question)? A) Guy on left B) Guy on right C) I don’t know D) Same How to get TIR in prism. Looking at complementary angles inside the triangles we have 90-2 + 90-3 = 120 2 + 3 = 60 As 1 increases 2 increases (snell’s law) and 3 decreases Avoid TIR as 1 increases Serway 35-44, Solve on Board A triangular glass prism with apex angle F = 60.0° has an index of refraction n = 1.50 (Fig. P35.43). What is the smallest angle of incidence 1 for which a light ray can emerge from the other side? Optical Fibers Protective Jacket Low n glass High n glass •Light enters the high index of refraction glass •It totally internally reflects – repeatedly •Power can stay largely undiminished for many kilometers •Used for many applications •Especially high-speed communications – up to 40 Gb/s Chapter 36 Mirrors and Lenses Lenses and Mirrors Summarized •The front of a lens or mirror is the side the light goes in R>0 p>0 q>0 Concave Object Image mirrors front in front in front lenses f f 12 R 1 1 Convex Object Image 1 n2 1 front in front in back f n1 R1 R2 1 1 1 p q f Variable definitions: •f is the focal length •p is the object distance from lens •q is the image distance from lens •h is the height of the object •h’ is the height of the image •M is the magnification h q M h p Other definitions: •q > 0 real image •q < 0 virtual image •M > 0 upright •M < 0 inverted Summary of Geometric Optics Rules 1. Object distances, p are always positive (except in the case of more than one lens or mirror when the first image is on the far side of the second lens or other cases where you have a virtual object like object behind mirror). 2. Image distances, q, are positive for real images and negative for virtual images. 3. Real images form on the same side of the object for mirrors and on the opposite side for refracting surfaces (lenses). Virtual images form on the opposite side of the object for mirrors and on the same side for refracting surfaces. 4. When an object faces a convex mirror or concave refracting surface the radius of curvature, R, is negative. When an object faces a concave mirror or convex refracting surface the radius of curvature is positive. Object object location image location image type image orientation Plane mirror anywhere virtual Concave mirror concave mirror convex mirror converging lens (convex) converging lens diverging lens inside f opposite object opposite virtual same object same outside f same real anywhere opposite inside f sign of f sign of R sign of q (R1 for lens) sign of m ∞ negative =+1 positive positive negative positive inverted positive positive positive negative virtual same negative negative negative positive same virtual same positive positive negative positive outside f opposite real inverted positive positive positive negative anywhere same virtual same negative negative negative positive as f=∞