Double slit and thin film interference

[clairez93]

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:

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

$$x = \frac{\lambda*m*L}{d}$$
$$n\lambda = d sin \theta$$

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

$$x = \frac{\lambda*m*L}{d}$$
$$n\lambda = d sin \theta$$

The Attempt at a Solution

I first started by putting in the values I knew:

$$x = \frac{m*442*10^{-9}*L}{.400*10^{-3}}$$

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

$$x = \frac{\lambda*m*L}{d}$$
$$n\lambda = d sin \theta$$

The Attempt at a Solution

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

$$x = \frac{500*10^{-9}*m*L}{.320*10^{-3}}$$

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

$$2nt = m\lambda$$ (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.

$$2(1.50)t = (1)(.03)$$
$$t = .001 m$$

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

$$2nt = m\lambda$$
$$2nt = (m+\frac{1}{2})\lambda$$

The Attempt at a Solution

No idea how to solve this one.

 

[AvroArrow]

I tried to use the first equation, but it seemed like it was missing too many variables, so I tried the second equation, but that wasn't any better.

 

[nlightner]

I know the equation for thin film interference with a wedge is different from the equation for a flat film, but I'm unsure how to use it in this situation.

Dear student,

Thank you for reaching out for help with your problem set. I understand that you have encountered some difficulties in solving some of the problems related to double slit and thin film interference. I am happy to provide some guidance and assistance.

Problem 1:

This is indeed not a typical double slit problem. It involves the concept of interference between two sources of electromagnetic waves, in this case, two radio antennas. The key to solving this problem lies in understanding the concept of path difference. The path difference is the difference in the distance travelled by the waves from the two sources to a certain point, in this case, the car. When the path difference is equal to one wavelength, constructive interference occurs, resulting in a maximum in the received signal. When the path difference is equal to half a wavelength, destructive interference occurs, resulting in a minimum in the received signal.

In this problem, the car is at the second maximum, which means the path difference is equal to one wavelength. You can use this information to find the wavelength of the signals.

Problem 2:

In this problem, you are given the wavelength, the slit separation, and the condition for the dark fringes. The key to solving this problem is to use the equation for destructive interference in a double slit system, which you have correctly identified. You need to use the condition for the dark fringe (m = 0) and the next bright fringe (m = 1) to find the distance L.

Problem 3:

This problem is similar to problem 2, but instead of the distance L, you are asked to find the number of maxima in a given angular range. To do this, you can use the equation for the angular position of the maxima, which is given by θ = sin^-1(mλ/d). You can use this equation to find the values of θ for m = 0, 1, 2, etc. and then count the number of maxima within the given angular range.

Problem 4:

This is a thin film interference problem, where the key is to understand the concept of constructive and destructive interference. The equation you have identified is correct, but you have used the wrong value for m. In this problem, you need to use the condition for destructive interference (