In searching the bottom of a pool at night, a watchman shines a narrow beam of l

Question

In searching the bottom of a pool at night, a watchman shines a narrow beam of light from his flashlight, 1.3?m above the water level, onto the surface of the water at a point d = 2.9m from his foot at the edge of the pool (Figure 1) .

Where does the spot of light hit the bottom of the h = 2.1-m-deep pool? Measure from the bottom of the wall beneath his foot.

In searching the bottom of a pool at night, a watchman shines a narrow beam of light from his flashlight, 1.3?m above the water level, onto the surface of the water at a point d = 2.9m from his foot at the edge of the pool (Figure 1) . Where does the spot of light hit the bottom of the h = 2.1-m-deep pool? Measure from the bottom of the wall beneath his foot.

Explanation / Answer

Here,

the angle of incidence is

i = arctan(2.9/1.3)

i = 65.9 degree

Now, using snell's law

1.33 * sin(r) = sin(65.9) *1

r = 43.3 degree

Now, for h = 2.1 m

total distance = 2.9 + h*tan(43.3)

total distance = 2.9 + 2.1 * tan(43.3)

total distance =4.88 m

the spot of light hit the bottoma at 4.88 m away

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