You come across a water-filled pothole in a parking lot. The pothole is 5 feet i

Question

You come across a water-filled pothole in a parking lot. The pothole is 5 feet in

diameter and 6 inches deep. The water surface is smooth and still, and has a thin film

of oil (refractive index noil = 1.5) on it (see figure, the dimensions and angles in the

figure are not to scale). You view the sun

You come across a water-filled pothole in a parking lot. The pothole is 5 feet in diameter and 6 inches deep. The water surface is smooth and still, and has a thin film of oil (refractive index noil = 1.5) on it (see figure, the dimensions and angles in the figure are not to scale). You view the sun's reflection in the puddle such that your eye and the sun both appear at an angle ?=20o from the vertical. Part of the incident light from the sun is reflected at point A on the surface between air and oil, and the rest of the light is transmitted (and refracted) into the oil film and partially reflected at point B on the second surface between oil and water. The latter part of the light will travel back to hit the first surface at point C. The directly reflected part of the sun light and the transmitted and then reflected part of the light interfere in your eye. The reflection of the sun appears blue in your eye. Do the reflected and transmitted/reflected light waves of this color interfere constructively or destructively in your eye? Explain briefly. Blue light has a wavelength of ?blue=450 nm in air. What is the wavelength of the blue light in the film of oil? What is the angle ? under which the blue light is transmitted into the oil film? In the textbook in section 24.it is mentioned that when light travels from a medium of lower refractive index to a medium of higher index, the part of the light that reflects changes its phase by 180o. This phase change acts (for interference purposes) the same as a path difference of ?/2. On the other hand, if the light wave is traveling from a medium with a higher index to one with a lower index, no phase change occurs. Briefly explain both situations in your own words using sketches of incident and reflected waves at a surface. Then explain whether or not a phase change will occur at either of the two surfaces (air-oil, oil-water) in the puddle. What angle ? Should use if you want to see green (?green=550 nm) reflected? When you look at an ordinary oil slick, you see bands of many colors rather than one single color. What effects might account for this? The transmitted part of the light travels an extra distance ABC. How long is this distance in terms of the thickness t of the oil film and the angle ?? In order to interfere constructively in your eye the directly reflected wave at point A and the transmitted wave at point C must be in phase. (We neglect any further path length difference between the air-oil surface and your eye). How thick is the oil film such that the light appears blue for you? (Careful, you need to consider your result from part 3 here!) A drop of oil is about 0.1 ml. How many drops of oil are in the oil film of the puddle? What angle ? should you use if you want to see green (?green=550 nm) reflected? When you look at an ordinary oil slick, you see bands of many colors rather than one single color. What effects might account for this?

Explanation / Answer

a) destructively. because we see the colour which is obsorbed by matarial or which is not present in light.

b) 450/1.5 = 300 nm

sin(alpha) = sin(20)/1.5

angle = 13.2o

c)air-oil : phase will change by 180o

oil-water: no phase change will occur

d) distance = 2*d*sec(alpha) = 2d*sec(13.2o)

e) For destructive interfarance = 2dsec(13.2) = n*450*10^-9

d = n*(450*10^-9/2sec(13.2)

= 219.05*n nm

f)2.5^2*pi*0.5*(0.3)^3/(0.1*10^-6) =2650719 approx

g)sec(angle)/sec(13.2) = 550/450

angle = 37o

h) because The water surface is smooth and still here. but in ordinary case surface is not used to be smooth and still. so thikness and angle vary with time and length. so we see bands of many colors rather

than one single color

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