Question

An observer in a small boat is floating on the surface of a large lake with clear, but contaminated water with index of refraction n = 1.38. Nearby is a wooden post emerging from the water which is embedded in the lake bottom, a distance h = 7.20 meters below the water's surface. What is the maximum distance from the post at which the observer would be able to see the bottom of the post?

Answer 1

the answer will be 6.847m

Answer 2

i wanna explain my procedure to solve this problem

Answer 3

\[n=\frac{ 1 }{ \sin \theta _{c} }\]

Answer 4

here n=refractive index of water

Answer 5

\[\theta _{c}=critical \angle\]

Answer 6

\[or, 1.38=\frac{ 1 }{ \sin \theta _{c} }\]

Answer 7

\[or, \sin \theta _{c}=\frac{ 1 }{ 1.38 }\]

Answer 8

\[\theta _{c}=\sin^{-1} \frac{ 1 }{ 1.38 }\]

Answer 9

\[or, \theta _{c}=0.8105084862\]

Answer 10

now

Answer 11

\[\tan \theta=\frac{ 7.20 }{ d }\]

Answer 12

here 7.20m is the length of the woden post
d= distance frm the post to observer

Answer 13

\[or, d=\frac{ 7.20 }{ \tan \theta _{c} }\]

Answer 14

\[or, d=\frac{ 7.20 }{ \sin.8105084862 }=6.847m\]

Answer 15

if u need more explanation then u can ask me