How Do You Solve These Advanced Optics Problems?

[slaw155]

Hi

I have been trying to work these out over the last few days and can get part way through but not get to the final answer. So some help would be appreciated http://www.thephysicsforum.com/images/smilies/smile.png

1. An unpolarised light beam of 2mm diameter carrying 4mW of power passes through two polarisers. The intensity after the second polarizer is 75W/m^2. What is the angle between the axes of the two polarisers?
I'm thinking: initial intensity = power/area = 4mW/(4 x pi x (2mm)^2), and then you use final intensity = initial intensity x (cosx)^2, however this gives me the wrong answer from the textbook answer of 70degrees.

2. A diverging lens of focal length 6mm produces an image of magnification of 1/2. What is the distance between the object and lens?
I have no idea how to approach this besides knowing 1/f = 1/di + 1/do and magnification = -di/do (correct answer = 6mm)

3. How many dark fringes can be observed in the diffraction pattern produced by a single slit of width 2.3micrometres with green light of wavelength 535m?
They don't give us the angle so I don't know how to use the formula dsinx= m x wavelength here. (correct answer = 8)

Thanks again

 

[Orodruin]

Generally, I would suggest making one thread per question. This will make it easier to help you and keep discussing only one problem per thread instead of mixing them all up. Anyway ...

1. An unpolarised light beam of 2mm diameter carrying 4mW of power passes through two polarisers. The intensity after the second polarizer is 75W/m^2. What is the angle between the axes of the two polarisers?
I'm thinking: initial intensity = power/area = 4mW/(4 x pi x (2mm)^2), and then you use final intensity = initial intensity x (cosx)^2, however this gives me the wrong answer from the textbook answer of 70degrees.

Hint: What is the intensity of the light in between the polarisers?

2. A diverging lens of focal length 6mm produces an image of magnification of 1/2. What is the distance between the object and lens?
I have no idea how to approach this besides knowing 1/f = 1/di + 1/do and magnification = -di/do (correct answer = 6mm)

You have two equations and two unknowns, did you try to solve this system of equations?

3. How many dark fringes can be observed in the diffraction pattern produced by a single slit of width 2.3micrometres with green light of wavelength 535m?
They don't give us the angle so I don't know how to use the formula dsinx= m x wavelength here. (correct answer = 8)

How is the light going to be dispersed after passing through the slit? (I.e., in what directions relative to the slit will there be light?) What is the angular difference between the fringes?

 

[slaw155]

Generally, I would suggest making one thread per question. This will make it easier to help you and keep discussing only one problem per thread instead of mixing them all up. Anyway ...
Hint: What is the intensity of the light in between the polarisers?You have two equations and two unknowns, did you try to solve this system of equations?How is the light going to be dispersed after passing through the slit? (I.e., in what directions relative to the slit will there be light?) What is the angular difference between the fringes?

Q1. I used the formula intensity between polarisers = initial intensity x (cosx)^2 with x=0degrees and initial intensity = P/A where A=4 x pi x r^2, and then used this as the initial intensity in intensity after 2nd polariser = intensity between polarisers x (cosx)^2 but this still gives me the wrong answer? Is my method of calculating initial intensity correct or is there a different formula to use rather than Area being area of a sphere in P/A?
Q2. I did try to solve the two equations together, ended up with a quadratic equation, which I solved to give distance = 0.66mm, which is wrong compared to the correct answer of 6mm?
Q3. After considering your questions I thought the angle x in dsinx=n x wavelength must be 90degrees but this still does not work.

 

[Orodruin]

Q1. Your incoming light is unpolarized, meaning it comes in an equal combination of both polarizations. How does this affect your results?
Q2. I have not done it explicitly so I cannot offer more advice than that I gave in my previous point.
Q3. Let us start from the beginning, what is the spread angle of the light after the slit?

 

[HalfLostAndSearching]

for any help!

Hi there,

I can understand how these problems may be challenging. Let's take a look at each one individually and see if we can work through them together.

1. For the first problem, you are on the right track with using the formula for intensity. However, remember that the intensity of light passing through a polarizer is given by I = I0cos^2θ, where θ is the angle between the polarizer's axis and the direction of polarization of the incoming light. So, in this case, we have an initial intensity of 4mW/(4π(2mm)^2) and a final intensity of 75W/m^2. We can set these equal to each other and solve for θ, which should give us the angle between the axes of the two polarizers.

2. For the second problem, you are correct in using the lens equation and the magnification equation. The key here is to remember that the magnification is negative for a diverging lens, so your equation should be -di/do = -1/2. From there, you can solve for do to find the distance between the object and the lens.

3. For the third problem, the formula dsinθ = mλ is used to calculate the angles at which the bright fringes occur in a diffraction pattern. However, for dark fringes, the formula is slightly different: dsinθ = (m + 1/2)λ. So, in this case, we can plug in the given values and solve for m to find the number of dark fringes.

I hope this helps and good luck with your problem-solving!