Young's double slit experiment with two wavelengths of light

Question

I know that a double-slit experiment pattern for blue, and red light individually gives the intensity patterns easily found in textbooks. But I fail to understand the exact pattern produced by a double-slit experiment where both red AND blue light is used.

My question: When there is a question where it states that a light source is used where it emits both blue and red light in the following setup. And assume that red light is $1.5\lambda$ and blue light is $\lambda$, what is the intensity pattern observed on the screen?

I do not get a good visual representation of what will occur, but I do get approaching this by merging the intensity pattern for the blue light and red light individually. But cannot exactly describe the shape. I would appreciate the explanation.

Answer 1

We would get the superposition of a red double slit pattern with a blue double slit pattern. The minima of the red one are spaced wider apart than those of the blue one by a factor of 1.5. If we do the experiment with white light we get color fringes.

Answer 2

The separate patterns just overlay each other. Here is an example with Red, Green and Blue. Notice how the blue starts earlier, followed by the green and then red.

Answer 3

For the sake of simlicity, let us forget about polarization and consider a scalar problem. Let us imagine that, at a certain point, two signals are interposed: $S_1=A_1\cos(\omega_1 t+\alpha_1)$ and $S_2=A_2\cos(\omega_2 t+\alpha_2)$ ($S_1$ and $S_2$ can be, for example, some component of the electrical field). The intensity will be proportional to $$(S_1+S_2)^2=$$ $$=A_1^2\cos^2(\omega_1 t+\alpha_1)+A_2^2\cos^2(\omega_2 t+\alpha_2)+2 A_1 A_2\cos(\omega_1 t+\alpha_1)\cos(\omega_2 t+\alpha_2)=$$ $$=A_1^2\cos^2(\omega_1 t+\alpha_1)+A_2^2\cos^2(\omega_2 t+\alpha_2)+$$ $$+A_1 A_2(cos((\omega_1+\omega_2) t+\alpha_1+\alpha_2)+cos((\omega_1-\omega_2) t+\alpha_1-\alpha_2).$$ When the intensity is averaged over time, the resulting intensity is the sum of intensities for the fields of frequencies $\omega_1$ and $\omega_2$ acting separately, as other answers state. Note however that there is also beating, which is observed experimentally when the frequencies $\omega_1$ and $\omega_2$ are close. Please also note that the above calculation does not take into account the physiology of the human eye, which can see a combination of red and blue colors as some color that is different from both of these colors (see the picture in @Bill Alsept's answer).