# Interference and slits question

• doctordiddy
In summary, the problem involves a radar tower of a certain height, sending out a signal of a certain wavelength. A weather balloon is released from a boat at a certain distance from the tower and floats up to a certain altitude. Due to interference with reflections off the water, certain wavelengths will be weak when they reach the balloon. The task is to find the maximum wavelength for destructive and constructive interference. To do this, one must find the pathlengths from the tower to the balloon in terms of the position where the ray reflects from the water.
doctordiddy

## Homework Statement

A radar tower sends out a signal of wavelength . It is meters tall, and it stands on the edge of the ocean. A weather balloon is released from a boat that is a distance out to sea. The balloon floats up to an altitude . 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?

What is the maximum wavelength that will interfere constructively

http://session.masteringphysics.com/problemAsset/1010843/27/98393A.jpg

## The Attempt at a Solution

I'm not quite sure what to do, I know that for these questions you typically want to find deltad. I'm assuming once you find deltad you can equate it to lambda/2 (destructive interference) and then multiply the deltad by 2 to get lambda? So I guess my problem is I'm not sure how to find the deltad and how to tell whether it is the maximum wavelenght or not. Can anyone help me out/give me tips?

thanks

ps the answer is for part a is 2x(h/d), i don't know how to get there however..

Find the yellow and orange pathlengths in terms of the position (y) where the ray reflects from water in terms x, h, d, from the right triangles you find in the figure.

ehild

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## 1. What is interference?

Interference is a phenomenon observed when two or more waves meet at the same point in space and time. It occurs when the waves are of the same frequency and interfere constructively or destructively, resulting in an overall change in the amplitude or intensity of the wave.

## 2. How does interference occur in the context of slits?

In the context of slits, interference occurs when a single wave passes through two or more narrow openings or slits. This results in the wave diffracting and creating an interference pattern on a screen or surface behind the slits.

## 3. What is the difference between constructive and destructive interference?

Constructive interference occurs when two waves meet and their amplitudes add together, resulting in a larger overall amplitude. This is seen as bright fringes in an interference pattern. Destructive interference, on the other hand, occurs when two waves meet and their amplitudes cancel out, resulting in a smaller overall amplitude. This is seen as dark fringes in an interference pattern.

## 4. How does the distance between slits affect interference?

The distance between slits, also known as the slit spacing, plays a crucial role in interference. When the slit spacing is small compared to the wavelength of the wave, the interference pattern will have a wide central maximum and narrow secondary maxima. When the slit spacing is large compared to the wavelength, the interference pattern will have a smaller central maximum and wider secondary maxima.

## 5. How is the interference pattern affected by changing the wavelength of the wave?

The interference pattern is directly affected by the wavelength of the wave. When the wavelength is increased, the distance between maxima in the interference pattern also increases. When the wavelength is decreased, the distance between maxima decreases. This is because the wavelength determines the spacing between the wavefronts, which affects how the waves interfere with each other.

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