3. Inferior Mirages. On a brilliant spring day, the air temperature is 20 °C, bu
ID: 1790592 • Letter: 3
Question
3. Inferior Mirages. On a brilliant spring day, the air temperature is 20 °C, but the temperature of the air right next to an asphalt-covered road is 50 °C. The refractive index of air is 1.00027 at 20°C and 1.00024 at 50 °C, due to the decrease in density on heating. What is the minimum angle of incidence of light from a car's headlight onto the cold air/warm air interface that will result in total reflection? Is your result consistent with your observation of headlights reflecting from "puddles" on the highway on sunny days?
Explanation / Answer
air at 20oC is more denser than the air at 50oC
n1 = 1.00027 at 20oC
n2 = 1.00024 at 50oC
during total internal reflection the refracted ray grazes along interface
making angle of refraction as 90
from snells law
n1*sintheta1 = n2*sintheta2
theta2 = 90
1.00027*sintheta1 = 1.00024*sin90
theta1 = 89.55 degrees
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