Question

The sun is 60° above the horizon. Rays from the sun strike the still surface of a pond and cast a shadow of a stick that is stuck in the sandy bottom of the pond. If the stick is 19 cm tall, how long is the shadow?

Answer 1

shadow length 7.67 cm

Step-by-step explanation:

given data:

refractive index of water is 1.33

by snell's law we have

`n_(air) sin30 =n_(water) sin\theta`

`1*0.5 = 1.33*sin\theta`

solving for
`\theta`

`sin\theta = (3)/(8)`

`\theta = sin^(-1)(3)/(8)`

`\theta =  22 degree`

from shadow- stick traingle

`tan(90-\theta) = cot\theta = (h)/(s)`

`s = (h)/(cot\theta) = h tan\theta`

s = 19tan22 = 7.67 cm

s = shadow length