- #1

clairez93

- 114

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While completing my problem set for this chapter, I came across 5 problems I could not solve. I thought it might be rather annoying if I posted six posts, so I'm putting all my work and such here. I don't expect one person to try to help me with all of them, just one or two at a time will do, thank you. :]

Problem 1:

Two radio antennas separated by 300 m as shown in the figure [interference.jpg] simultaneously broadcast identical signals at the same wavelength. A radio in a car traveling due north receives the signals. (a) If the car is at the position of the second maximum, what is the wavelength of the signals? (b) How much frather must the car travel to encounter the next minimum in reception (Note: Do not use the small angle approximation in this problem)

[tex]x = \frac{\lambda*m*L}{d}[/tex]

[tex]n\lambda = d sin \theta[/tex]

No idea how to try this one, didn't seem like a typical double slit problem.

Problem 2:

Light with a wavelength of 442 nm passes through a double slit system that has slit separation d = 0.400 mm. Determine how far away a screen must be placed so that a dark fringe appears directly opposite both slits, with just one bright fringe between them.

[tex]x = \frac{\lambda*m*L}{d}[/tex]

[tex]n\lambda = d sin \theta[/tex]

I first started by putting in the values I knew:

[tex]x = \frac{m*442*10^{-9}*L}{.400*10^{-3}}[/tex]

Of course I think we'll have to eventually solve for L, but I am unsure what the m would be so that the fringe appears directly opposite both slits.

Problem 3:

Two slits are separated by 0.320 mm. A beam of 500-nm light strikes the slits, producing an interference pattern. Determine the number of maxima observed in the angular range -30 degrees < theta < 30 degrees.

[tex]x = \frac{\lambda*m*L}{d}[/tex]

[tex]n\lambda = d sin \theta[/tex]

Using the first equation, I again put in what I knew.

[tex]x = \frac{500*10^{-9}*m*L}{.320*10^{-3}}[/tex]

I'm again unsure what to put for m, also L is not given either. Missing variables missing variables.

Problem 4:

A possible means for making an airplane invisible to radar is to coat the plane with an antireflective polymer. If radar waves have a wavelength of 3.00 cm and the index of refraction of the polymer is n = 1.50, how thick would you make the coating?

[tex]2nt = m\lambda[/tex] (equation for thin film destructive interference if I'm not mistaken)

I actually got an answer for this one, albeit the wrong answer.

[tex]2(1.50)t = (1)(.03)[/tex]

[tex]t = .001 m [/tex]

Book answer: .500 cm

Problem 5:

An air wedge is formed between two glass plates separated at one edge by a very fine wire, shown in the figure [thinfilm.jpg]. When the wedge is illuminated from above by 600-nm light, 30 dark fringes are observed. Calculate the radius of the wire.

[tex]2nt = m\lambda[/tex]

[tex]2nt = (m+\frac{1}{2})\lambda[/tex]

No idea how to solve this one.

Problem 1:

## Homework Statement

Two radio antennas separated by 300 m as shown in the figure [interference.jpg] simultaneously broadcast identical signals at the same wavelength. A radio in a car traveling due north receives the signals. (a) If the car is at the position of the second maximum, what is the wavelength of the signals? (b) How much frather must the car travel to encounter the next minimum in reception (Note: Do not use the small angle approximation in this problem)

## Homework Equations

[tex]x = \frac{\lambda*m*L}{d}[/tex]

[tex]n\lambda = d sin \theta[/tex]

## The Attempt at a Solution

No idea how to try this one, didn't seem like a typical double slit problem.

Problem 2:

## Homework Statement

Light with a wavelength of 442 nm passes through a double slit system that has slit separation d = 0.400 mm. Determine how far away a screen must be placed so that a dark fringe appears directly opposite both slits, with just one bright fringe between them.

## Homework Equations

[tex]x = \frac{\lambda*m*L}{d}[/tex]

[tex]n\lambda = d sin \theta[/tex]

## The Attempt at a Solution

I first started by putting in the values I knew:

[tex]x = \frac{m*442*10^{-9}*L}{.400*10^{-3}}[/tex]

Of course I think we'll have to eventually solve for L, but I am unsure what the m would be so that the fringe appears directly opposite both slits.

Problem 3:

## Homework Statement

Two slits are separated by 0.320 mm. A beam of 500-nm light strikes the slits, producing an interference pattern. Determine the number of maxima observed in the angular range -30 degrees < theta < 30 degrees.

## Homework Equations

[tex]x = \frac{\lambda*m*L}{d}[/tex]

[tex]n\lambda = d sin \theta[/tex]

## The Attempt at a Solution

Using the first equation, I again put in what I knew.

[tex]x = \frac{500*10^{-9}*m*L}{.320*10^{-3}}[/tex]

I'm again unsure what to put for m, also L is not given either. Missing variables missing variables.

Problem 4:

## Homework Statement

A possible means for making an airplane invisible to radar is to coat the plane with an antireflective polymer. If radar waves have a wavelength of 3.00 cm and the index of refraction of the polymer is n = 1.50, how thick would you make the coating?

## Homework Equations

[tex]2nt = m\lambda[/tex] (equation for thin film destructive interference if I'm not mistaken)

## The Attempt at a Solution

I actually got an answer for this one, albeit the wrong answer.

[tex]2(1.50)t = (1)(.03)[/tex]

[tex]t = .001 m [/tex]

Book answer: .500 cm

Problem 5:

## Homework Statement

An air wedge is formed between two glass plates separated at one edge by a very fine wire, shown in the figure [thinfilm.jpg]. When the wedge is illuminated from above by 600-nm light, 30 dark fringes are observed. Calculate the radius of the wire.

## Homework Equations

[tex]2nt = m\lambda[/tex]

[tex]2nt = (m+\frac{1}{2})\lambda[/tex]

## The Attempt at a Solution

No idea how to solve this one.