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In talking about interference, particularly with light, you will most likely speak in terms of phase differences, as well as wavelength differences. In the mathematical description of a sine wave, the phase corresponds to the argument of the sine function. For example, in the function y=Asin(kx), the value of kx at a particular point is the phase of the wave at that point. Recall that in radians a full cycle (or a full circle) corresponds to 2π radians. How many radians would the shift of half a wavelength from the previous part correspond to?

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Answer:

[tex]\pi[/tex] radian

Explanation:

We are given that

Wavelength=[tex]\lambda[/tex]

We have to find the phase difference when the wavelength is equal to half of the initial wavelength.

Path difference=[tex]\Delta x=\frac{\lambda}{2}[/tex]

For interference

Phase difference=[tex]\frac{2\pi}{\lambda}\times \Delta x[/tex]

Substitute the value

Phase difference=[tex]\frac{2\pi}{\lambda}\times\frac{\lambda}{2}[/tex]

Phase difference=[tex]\pi[/tex] radian

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