A submarine is 2.81 times 10^2 m horizontally from shore and 1.00 times 10^2 m b

Question

A submarine is 2.81 times 10^2 m horizontally from shore and 1.00 times 10^2 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 2.48 times 10^2 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. (The index of refraction of water is n = 1.333.) Find the angle of incidence of the beam striking the water air interface. (Give your answer to at least one decimal place.) Find the angle of refraction. (Give your answer to at least one decimal place.) What angle does the refracted beam make with respect to the horizontal? (Give your answer to at least one decimal place.) Find the height of the target above sea level.

Explanation / Answer

b) tan i = (281-248)/100 = 0.33

i = tan-1 (0.33)= 18.26 degree

c) By snells law,

n1 sin i = n2 sin r

1.333 sin 18.26 degree = 1 sin r

0.4176 = sin r

r = 24.69 degree

d) angle refracted ray makes with horizontal = 90- 24.69 = 65.31 degree

e)tan 65.31 degree = h/248

h = 248 * 2.175 = 539.4 m

hence height of target is 539.4m

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