How Does Reflection Affect Radar Signal Interference at Sea?

[deathslayer7]

Homework Statement

A radar tower sends out a signal of wavelength lambda. It is x meters tall, and it stands on the edge of the ocean. A weather balloon is released from a boat that is a distance d out to sea. The balloon floats up to an altitude h. In this problem, assume that the boat and balloon are so far away from the radar tower that the small angle approximation holds.

Due to interference with reflections off the water, certain wavelengths will be weak when they reach the balloon. What is the maximum wavelength that will interfere destructively?
Express your answer in terms of x, h, and d.

Homework Equations

maxium deconstructive interference. delta r=m*lambda. Could be wrong though.

The Attempt at a Solution

I extended (lambda 2) the blue line so it reaches down to the height where the radio tower would be if it was reversed.

I solved for Lamda 1 and 2 getting,

L1^2=h^2 - 2*h*x + x^2 + d^2

L2^2=h^2 + 2*h*x +x^2 + d^2

find delta r by subtracting.

L2 - L1 = sqrt(h^2 + 2*h*x +x^2 + d^2) - sqrt(h^2 - 2*h*x +x^2 + d^2)=lambda/2

lambda= 2*[sqrt(h^2 + 2*h*x +x^2 + d^2) - sqrt(h^2 - 2*h*x +x^2 + d^2)]

but I am doing something wrong. Any help is appreciated.

 

[ehild]

The wave suffers pi phase change when it is reflected from a medium of higher refractive index than that of the medium of incidence.

ehild