Question
gotten yourself stranded in a remote wilderness you must live off the land while you wait for rescue. One morning, you attempt to spear a fish tor breakfast. You spot a fish in a shallow river. Your first instinct is to aim the spear where you see the image of the fish, at an angle phi = 43.40 degree with respect to the vertical as shown in figure. However, you know from physics class that you shouldn't throw the spear at the image of the fish, because the actual location of the fish is farther down than it appears, at a depth of H = 0.9000 m. This means you must decrease the angle at which you throw the spear. This slight decrease in the angle is represented as alpha in the figure. If you throw the spear from a height h = 1, 100 m above the water, calculate the angle decrease alpha, Assume that the index of refraction is 1.000 for air and 1.330 for water.
Explanation / Answer
using snell's law
1.33 sini = 1 sin43.4
sini = sin43.4 / 1.33
i = sin-1 ( 0.5166 )
i = 31.1o
tani = x1 / H
tan31.1 = x1 / 0.9
x1 = 0.5429
tan43.4 = x2 / h
tan43.4 = x2 / 1.1
x2 = 1.040
now
tan ( 43.4 - ) = ( x1 + x2 ) / ( h + H )
tan ( 43.4 - ) = ( 0.5429 + 1.040 ) / ( 1.1 + 0.9 )
tan ( 43.4 - ) = 0.79145
( 43.4 - ) = 38.3598
= 5.0402o
