Interference in a Double-Slit Experiment

[annikaw]

In a double-slit experiment, the distance between slits is 5.0mm and the slits are 1.0m from the screen. Two interference patterns can be seen on the screen: one due to light of wavelength 480nm, and the other due to light of wavelength 600nm. What is the separation on the screen between the third-order (m=3) bright fringes of the two interference patterns?

From my notes, I find that $d\sin\theta=m\lambda$.

However, I do not know how to get values of $\theta$ that can be put to the equation to find the difference in separation.

 

[I like Serena]

In a double-slit experiment, the distance between slits is 5.0mm and the slits are 1.0m from the screen. Two interference patterns can be seen on the screen: one due to light of wavelength 480nm, and the other due to light of wavelength 600nm. What is the separation on the screen between the third-order (m=3) bright fringes of the two interference patterns?

From my notes, I find that $d\sin\theta=m\lambda$.

However, I do not know how to get values of $\theta$ that can be put to the equation to find the difference in separation.

Hi annikaw! Welcome to MHB! (Smile)

Let's get a drawing of the situation:
View attachment 4506

We get a bright fringe when $d\sin\theta=m\lambda$.
The corresponding position on the screen is $OP=D\sin\theta$.

Can you deduce where the 2 requested fringes are?