Question

A submarine is 309 m horizontally from the shore of a freshwater lake and 105 m beneath the surface of the water. A laser beam is sent from the submarine so that the beam strikes the surface of the water 227 m from the shore. A building stands on the shore, and the laser beam hits a target at the top of the building. The goal is to find the height of the target above sea level.

Required:
a. Draw a diagram of the situation, Identifying the two triangles that are important in finding the solution.
b. Find the angle of incidence of the beam striking the water-air interface.
c. Find the angle of refraction.
d. What angle does the refracted beam make with the horizontal?
e. Find the height of the target above sea level.

Answer 1

Answer:

Explanation:

a) See the attached file for diagram . The two triangles are ABC and DEC .

b )

Angle of incidence = i

Tan i = ( 309 - 227 ) / 105

= 82 / 105 = .78

i = 38°

c )

Sin i / sinr = 1 / μ where μ is refractive index of water .

Sin i / sinr = 1 / μ = 1 / 1.33

sin 38 / sinr = .7518

.6156 / sinr = .7518

sinr = .6156 / .7518

.819

r = 55°

d )

angle  the refracted beam makes with the horizontal = 90 - 55 = 35°

e )

h / 227 = Tan 35

h = 227 x Tan 35

= 159 m

Height required = 159 m .