Question

You are standing on the edge of a swimming pool and looking directly across at the opposite side. You notice that the bottom edge of the opposite side of the pool appears to be at an angle of 26.0° below the horizontal. However, when you sit on the pool edge, the bottom edge of the opposite side of the pool appears to be at an angle of only 13.2°below the horizontal. Use these observations to determine the width and depth of the pool. Hint: You will need to estimate the height of your eyes above the surface of the water when standing and sitting. (Assume 1.7 m when standing and 0.7 m when sitting.)

Width=__________ m

Depth=_________m

Answer 1

26 口; 13:27 en 2G 3.47 m て 13.2° 17.2

From Snell's law Refractive Index of water $\mu =\frac{sini}{sinr}$

Given $\mu =4/3$ and i₁ =26⁰ , $\Rightarrow$ r₁ = 19.2⁰

   In the second case i₂ = 13.2⁰ $\Rightarrow$ r₂ = 9.9⁰

From figure given above

      Tan26⁰ = 1.7/x

         x= 3.49m

Tan13.2⁰ = 0.7/x¹

          x¹ = 3.0m

In the second triangel in both the cases we have

   Tan19.2⁰=(w-x)/d and Tan9.9⁰ =w-x^')/d

      Now, Tan19.2⁰/Tan9.9⁰ = 2

       2=(w-x)/(w-x^')  

The width of the lake is

        w= 3.16m

         now, d= (w-x¹)/Tan9.9⁰ =(3.16-3)/0.175

             Depth of the lake d =0.91m