SSM In Fig 35-4, assume that two waves of light in air, of wavelength 400nm, are initially in phase. One travels through a glass layer of index of refraction n1 = 1.60 and thickness L. The other travels through an equally thick plastics layer of index of refraction n2 = 1.50. (a) What is the smallest value L should have if the waves are to end up with a phase difference of 5.65 rad? (b) if the waves arrive at some common point with the same amplitude, is their interference fully constructive, fully destructive, intermediate but closer to fully constructive but closer to fully destructive?
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- A linearly polarized microwave of wavelength 1.50 cm is directed along the positive x axis. The electric field vector has a maximum value of 175 V/m and vibrates in the xy plane. Assuming the magnetic field component of the wave can be written in the form B = Bmax sin (kx t), give values for (a) Bmax, (b) k, and (c) . (d) Determine in which plane the magnetic field vector vibrates. (e) Calculate the average value of the Poynting vector for this wave. (f) If this wave were directed at normal incidence onto a perfectly reflecting sheet, what radiation pressure would it exert? (g) What acceleration would be imparted to a 500-g sheet (perfectly reflecting and at normal incidence) with dimensions of 1.00 m 0.750 m?arrow_forwardIn Figure P37.52, suppose the transmission axes of the left and right polarizing disks are perpendicular to each other. Also, let the center disk be rotated on the common axis with an angular speed . Show that if unpolarized light is incident on the left disk with an intensity Imax, the intensity of the beam emerging from the right disk is I=116Imax(1cos4t) This result means that the intensity of the emerging beam is modulated at a rate four times the rate of rotation of the center disk. Suggestion: Use the trigonometric identities cos2=12(1+cos2) and sin2=12(1cos2). Figure P37.52arrow_forward*66 o In Fig. 33-62, a light ray in air is incident at angle 6, on a block of transparent plastic with an index of refraction of 1.56. The dimen- sions indicated are H= 2.00 cm and W = 3.00 cm. The light passes through the block to one of its sides and there undergoes reflection (in- side the block) and possibly refraction (out into the air). This is the point of first reflection. The re- flected light then passes through the block to another of its sides-a point of second reflection. If 6 = 40°, on which side is the point of (a) first reflection and (b) second reflection? If there is refraction at the point of (c) first reflection and (d) second reflection, give the angle of refraction; if not, answer "none." If 61 = 70°, on which side is the point of (e) first reflection and (f) second reflection? If there is refrac- tion at the point of (g) first reflection and (h) second reflection, give the angle of refraction; if not, answer “none." н Figure 33-62 Problem 66.arrow_forward
- -55 O SSM In Fig. 33-55, a 2.00- m-long vertical pole extends from the bottom of a swimming pool to a point 50.0 cm above the water. Sunlight is incident at angle e= Blocked sunrays 55.0°. What is the length of the shadow of the pole on the level bot- tom of the pool?arrow_forward77 E Rainbow. Figure 33-67 shows a light ray entering and then leaving a falling, spherical raindrop after one internal reflec- tion (see Fig. 33-21a). The final direction of travel is deviated (turned) from the initial direction of travel by angular deviation Bdev- (a) Show that 6sey is Odey = 180° + 20, – 48, where e, is the angle of incidence of the ray on the drop and 0, is the angle of refraction of the ray within the drop. (b) Using Snell's law, substitute for 6, in terms of 6, and the index of refraction n of the water. Then, on a graphing calculator or with a computer graphing package, graph Osey versus 0, for the range of possible 6; values and for n = 1.331 for red light (at one end of the visible spectrum) and n = 1.333 for blue light (at the other end). The red-light curve and the blue-light curve have different minima, which means that there is a different angle of minimum deviation for each color. The light of any given color that leaves the drop at that color's angle of…arrow_forward(c) The electric fields from two e/m waves are described by E1 = 10.0 cos(kr – wt) N/C and E2 = 15.0 cos(kr – wt + 60°) N/C. What is the phase of the resultant electric field (in degrees)? (d) Electrons moving at a speed of 30 m/s pass through a single slit of diameter 8.5 x 10-5 m. A diffraction pattern forms, due to the wave nature of the electrons. At what angle (in degrees) is the first-order minimum of this pattern located? (e) A neutron (with mass m, = 939.566 MeV/c²) is confined inside a nucleus of the most common isotop of iron, Fe. Assume the nucleus is spherical, and that the uncertainty in the position of the neutron is the diameter, not the radius, of the nucleus. What is the minimum uncertainty in the velocity of the neutron, in m/s?arrow_forward
- A ray of light travelling in glass having a refractive index nglass = 1.5, is incident at an angle 0, on the glass-air interface. If a thin layer of liquid (niquid = 1.33) is poured on the glass air interface, then at what angle would the ray emerge from the liquid -air interface? air (nair) air (Nair) liquid (njiquid) glass (ng) glass (ng) 90.0° 82.5° 48.3° 35.7° 45.6°arrow_forwardAstronomers observe the chromosphere of the Sun with a filter that passes the red hydrogen spectral line of wavelength 656.3 nm, called the Holine. The filter consists of a transparent dielectric of thickness d held between two partially aluminized glass plates. The filter is kept at a constant temperature. (a) Find the minimum value of d that will produce maximum transmission of perpendicular H light if the dielectric has an index of refraction of 1.400. (Enter your answer to one decimal place.) nm (b) If the temperature of the filter increases above the normal value increasing its thickness, what happens to the transmitted wavelength? (Assume the index of refraction of the dielectric remains constant.) ---Select--- (c) The dielectric will also pass what near-visible wavelength? One of the glass plates is colored red to absorb this light. nmarrow_forwardRefractive Index (n) is a ratio of the speed of light in a vacuum to the speed of light in materials such as glass, water, plastic, etc. Using Snell's Law, and given an air to glass interface with and angle of incidence of 15 degrees, what will be the angle of refractance R if the refractive index of the glass is 1.5 ? Snell's Law: n; (sin I) = n, (sin R) So, Sin R = n; (sin I) / n And, R = arcsin (n; (sin I) / n,) For each angle I, find angle R: 5. I=0, R = 6. I=45, R = 7. I= 60, R = 8. I = 75, R = = arcsin (1(.259)/1.5) = arcsin (.172) = 9.9 degrees Wavelength in Air- Light- Angle of Light -Wavelength in Glass Normal 90° R Air nj-1 Glassarrow_forward
- A ray of light travelling in glass having a refractive index nglass = 1.5, is incident at an angle 6, on the glass-air interface. If a thin layer of liquid (niquid = 1.23) is poured on the glass air interface, then at what angle would the ray emerge from the liquid-air interface? air (nair) air (nair) liquid (njiquid) glass (ng) glass (ng) 35.7° 90.0° O 45.6° 48.3° 82.5°arrow_forwardIn the figure, assume two waves of light in air, of wavelength 407 nm, are initially in phase. One travels through a glass layer of index of refraction n = 1.62 and thickness L. The other travels through an equally thick plastic layer of index of refraction n2 = 1.36. (a) What is the smallest value L in meters should have if the waves are to end up with a phase difference of 5.26 rad? (b) If the waves arrive at some common point with thsame amplitude, is their interference fully constructive, fully destructive, intermediate but closer to fully constructive, or intermediate but closer to fully destructive? (a) Number i Units (b)arrow_forwardProblem 9: Consider light passing from air into water. What is the ratio of its wavelength in water, λw, to its wavelength in air, λa?arrow_forward
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