Somewhere in a Rainbow By Kerrie Pratt Seeing
Somewhere in a Rainbow By: Kerrie Pratt
Seeing Rainbows 1. Reflection vs Refraction 2. The Rainbow Angle 3. The Secondary Bow 4. Three Bows
Reflection and Refraction
Seeing rainbows + Light from the sun is refracted and reflected by water droplets. This is what allows us to see the rainbows. + Fermat's Principle: Light follows a path which minimizes the total travel time.
Reflection of Light + We want to determine at what point, R, the ray will reflect off the surface. + Can assume the speed of the ray is constant
Minimizing the Distance that The Ray Travels:
Law of Reflection 1 For reflection, the angle of incidence (α) is equal to the angle of reflection (β).
Law of Reflection (continued) The distance (x) that minimizes L(x) is found by: Cannot use this value, since it gives a negative distance.
Ray Travels The Minimum Distance When: or
Refraction of Light + We cannot assume rays travel at a constant speed. + Speed of light in water is less than the speed of air.
Assumptions based on the Law of Refraction Medium with Lower refractive index ---> medium with higher refractive index, light bends toward the perpendicular of the surface between the medium. (as seen in figure 2) Works in the other direction as well
Refraction of Light (Continued) Assumptions: ca = the speed of light in air cw = the speed of light in water
Law of Refraction The time it takes for the ray to travel is:
Law of Refraction 1 The ratio of the sine of the angle of incidence to the sine of the angle of refraction is a constant.
The Rainbow Angle
Assumptions We Can Make + Raindrops are spheres + Rays can follow many different paths + Part of the ray is reflected and some of the ray is refracted + The tangent to the circle at a point is perpendicular to the radius of the circle through the point
Simplest Ray in a Rainbow Formation
+ As point A moves throughout the circle, the deflection angle changes + Total deflection of the ray is a function of the angle of incidence
Total Deflection from Figure 1
Graph of D(α) with one Deflection
Rainbow Angle + Rainbow ray: incidence angle of 59. 58° + Rainbow angle is 42. 5°
Secondary Bow
The Secondary Bow + Each reflection reduces the intensity of the ray + Rays that have two internal reflections may produce a secondary bow + Rays must enter the bottom half of the drop
Diagram for Secondary Bow
Graph of D(α) with Two Deflections
Additional Deflections
Additional Deflections Each time we add a deflection, we are adding (180 -2β) to the previous deflection function.
Third Rainbow + Can be seen in a lab + We rarely see them in the sky since they are so dim.
Critical Point for n Reflections
D(α) with Three Deflections
Questions?
References 1. Straffin Text (all figures are from the Straffin Text)
Credits Special thanks to all the people who made and released these awesome resources for free: + Presentation template by Slides. Carnival + Photographs by Unsplash
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