iving gotten yourself stranded in a remote wilderness area, you must live off th

Question

iving gotten yourself stranded in a remote wilderness area, you must live off the land while you wait for rescue One morning, you attempt to spear a fish for 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 ?-43.40% with respect to the vertical, as shown in the 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 ? in the figure. image If you throw the spear from a height h1.100 m above the water, calculate the angle decrease ?. Assume that the index of refraction is 1.000 for air and 1.330 for water Number 8.41

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  

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