Visibility in Optics: Integration help

[Master J]

In calculating the visibility of an non point source interfernce pattern, you integrate the following:

dI = (C/w)(cos^2[(ud/gL)(y-y_0)]).dy_0.

between w/2 and -w/2. C, u, d, g, l , y constants.

I'm finding this pretty tricky to integrate. Could someone help? Step by step would be really helpful.

 

[Unco]

Hi Master J,

In calculating the visibility of an non point source interfernce pattern, you integrate the following:

dI = (C/w)(cos^2[(ud/gL)(y-y_0)]).dy_0.

between w/2 and -w/2. C, u, d, g, l , y constants.

I'm finding this pretty tricky to integrate. Could someone help? Step by step would be really helpful.

As you have it written (and assuming you mean to say that "L" is a constant), this just amounts to evaluating $$\int_{-w/2}^{w/2} A\cos^2{\left(B(y-y_0)\right)} \, dy_0$$ for constants y, A and B. Then, using a substitution, this amounts to integrating $$\cos^2{x}$$. To do that, use the identity $$cos^2{x} = \frac{1}{2}(\cos{2x} +1)$$. Show your work so we know where abouts you're getting stuck.