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The figure shows two point sources of light, A and B. B emits light waves that are +π radians out of phase with the waves from A. A is 3λ from P. B is 5λ from P. (λ is the wavelength.) Find the phase difference between waves arriving at P from A and B. What kind of interference does this situation lead to at P?

 

This problem is not well defined as there is not information about the polarizations of both light sources to make some conclusions about the interference phenomenon.

 

Let we suppose that the light beams of both sources are polarized and have the same polarization directions or were initially generated from the some initial single light source.

Suppose “B emits light waves that are +π radians out of phase with the waves from A” means that Phase of A source have delay on π radians.

 

The distance difference at P, Δd, for the first, A, and the second, B, sources is Δd = 5λ – 3λ = 2λ.

In the phase units this distance difference give the phase shift: Δθ = 2λ * 2π/λ. = 4π radians.

So final phase difference between waves at P from A and B Δθ_f = Δθ – π = 4π – π = 3 π.

 

Coherent light sources gives for this phase difference the destructive interference as wave maximums overlap with wave minimums 

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7. Unpolarized light is passed through three successive Polaroid filters, each with its transmission axis at 45.0° to the preceding filter. What percentage of light gets through?

 

Unpolarized light lost ½ of the initial intensity I₀ after the first Polaroid filter.

To calculate the changes of the light intensity on the second and the third filters we have to use the formula 38.9

I _passed = I _preceding cos² θ = I _preceding cos² 45^ο = I _preceding ½

So, after the first filter: I₁=I₀/2,

After the second filter: I₂=I₁/2= I₀/4

After the third filter: I₃=I₂/2=I₀/8

Solution: 100%/8 = 12.5% of the initial light (intensity) gets through. 

 

7. Unpolarized light is passed through three successive Polaroid filters, each with its transmission axis at 45.0° to the preceding filter. What percentage of light gets through?

Unpolarized light lost Ѕ of the initial intensity I0 after the first Polaroid filter.
To calculate the changes of the light intensity on the second and the third filters we have to use the formula 38.9
I passed = I preceding cos2 = I preceding cos2 45 = I preceding Ѕ
So, after the first filter: I1=I0/2,
After the second filter: I2=I1/2= I0/4
After the third filter: I3=I2/2=I0/8
Solution: 100%/8 = 12.5% of the initial light (intensity) gets through.

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