Peoples Physics Book Version-2

http://www.ck12.org Chapter 17. Light Version 2

Question: Nisha stands at the edge of an aquarium 3.0m deep. She shines a laser at a height of 1.7m that hits the
water of the pool 8.1m from the edge. Draw a diagram of this situation. Label all known lengths.

a) How far from the edge of the pool will the light hit bottom?

b) If her friend, Marc, were at the bottom and shined a light back, hitting the same spot as Nisha’s, how far from the
edge would he have to be so that the light never leaves the water?

Answer:

a) To solve for the distance from the edge we must first solve for the distance from the laser to the pool surface and
then add that to the distance from the pool surface to the bottom of the pool. We can find the distance from the laser
to the pool by using the Pythagorean Theorem.

a^2 +b^2 =c^2 ⇒b=

√

c^2 −a^2 = 8. 12 m− 1. 72 m= 7 .9m

Now that we have the length from the laser to the pull all we need is the length from the surface of the pool to the
bottom of it.

To find this value we will use the equation

na×sinθa=nw×sinθw

Once we have solved forθw, we will be able to use trigonometry to solve for the distance from the surface of the
pool to the bottom of the pool. We know thatna= 1 .00029 and thatnw= 1 .33. So once we solve forθa, we can
solve forθw.

sin−^1

1. 7

8. 1

= 12. 1 o

This is the complement ofθa, so

90 o− 12. 1 o= 77. 9 o

Now we can solve forθw.

na×sinθa=nw×sinθw⇒θw=sin−^1 (

na×sinθa

nw

) =sin−^1 (

1. 00029 ×. 98

1. 33

) = 47. 5 o