Assume that a light ray is refracted, then reflected, und then again refracted on a spherical drop of water, ccording to the figure.
Assume that a light ray is refracted, then reflected, und then again refracted on a spherical drop of water, ccording to the figure.
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Transcribed Image Text:P6. Rainbow
Assume that a light ray is refracted, then reflected,
and then again refracted on a spherical drop of water,
according to the figure.
Determine the total deviation angle d of the ray as the
function of the angle of incidence a. Make a plot of
the graph of this function.
Based on the previous calculation explain the for-
mation of rainbow and calculate the angle of the arcs
for different colors. (This is the angle at which the ob-
server sees a certain color with respect to the incident
ray coming from the Sun.)
The index of refraction of water is nred = 1.331 for
red light and nblue = 1.340 for blue light.
Expert Solution
Step 1:Determination of total deviation angle of the ray:
The primary rainbow is seen in the direction corresponding to the most dense clustering of rays leaving the drop after a single internal reflection. Subsequently, higher number of rainbowsfor k internal reflections,k=2,3,4,5..... Only primary and secondary are seen in nature.
The total deviation between the incident and emergent rays after k internal
reflections. Since each such reflection causes a deviation of ; (r = r(i) being the angle of
refraction, itself a function of i, the angle of incidence) and two refractions always occur, the total deviation is:
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