A researcher stands at the end of a lakeside pier,4.0 m above the water surface

Question

A researcher stands at the end of a lakeside pier,4.0 m above the water surface and 2d= 6.0 maway from a buoy floating on the lake in (Figure 1) . A rope hangs from the bottom of the buoy down into the water, with a light attached to its end. When the researcher looks at the light from a position at which his line of sight intersects the water surface exactly halfway between the pier and the buoy, the light appears to be d below the water surface.

Part A

How far under the surface is the light?

Express your answer with the appropriate units.

A researcher stands at the end of a lakeside pier,4.0 m above the water surface and 2d= 6.0 maway from a buoy floating on the lake in (Figure 1) . A rope hangs from the bottom of the buoy down into the water, with a light attached to its end. When the researcher looks at the light from a position at which his line of sight intersects the water surface exactly halfway between the pier and the buoy, the light appears to be d below the water surface.

Part A

How far under the surface is the light?

Express your answer with the appropriate units.

Explanation / Answer

Apparent depth = d = 3 m

Real depth = h

nw = index of refraction of water = 1.33

na = index of refraction of air

using the formula

nw /na = h/d

1.33 / 1 = h/3

h = 3.99 m = 4 m

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