A spotlight on a boat is y = 2.0 m above the water, and the light strikes the wa

Question

A spotlight on a boat is y = 2.0 m above the water, and the light strikes the water at a point that is x = 7.1 m horizontally displaced from the spotlight (see the drawing). The depth of the water is 4.0 m. Determine the distance d, which locates the point where the light strikes the bottom.
m

A spotlight on a boat is y = 2.0 m above the water, and the light strikes the water at a point that is x = 7.1 m horizontally displaced from the spotlight (see the drawing). The depth of the water is 4.0 m. Determine the distance d, which locates the point where the light strikes the bottom.

Explanation / Answer

the first set of information allows you to calculate the angle of incidence of the light to the water

draw a diagram representing this situation, remember that the angle of incidence is the angle with respect to the normal, and see that

tan(theta) = 8/2.5 => theta = 72.6 deg

now, use Snell's law to find the angle of refraction

n1 sin(theta1) = n2 sin(theta2)

n1 = n for air =1, theta1=72.6

n water = n2 = 1.33, so we have that the angle of refraction:

sin(theta2) = (1/1.33)sin72.6 => theta 2 =45.8 deg

draw another triangle representing the path of the light underwater, and see that

tan(theta2) = d/4 where d is the distance along the bottom, measured from the point where the light entered the water, to where the light strikes the bottom

or d = 4 tan 45.8 = 4.12m (which is 12.12 m from the boat)

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.