# Diffraction pattern vs Interference pattern

I am not confused with difference between Young's double slit experiment and diffraction.

In Young's double slit experiment, the interference pattern is bright fringes separated evenly with separation given by $$\Delta y=\frac{D\lambda}{d}$$ where $$D$$ is the slit-to-screen distance, $$d$$ is the slits separation and $$\lambda$$ is the wavelength.

Diffraction is pattern has a central maximum and the bright fringes on each side are not evenly separated, i.e. distance between 1st max and 2nd max does not equal to that between 2nd max and 3rd max.

Is the reason why Young's double slit experiment having an even fringes separation is that we treat the slit width to be so narrow that the light coming out from each slit can be treated as a point source (so this is just interference between two sources) ? However, in diffraction, we have a finite slit width, so the bright fringes are not evenly distributed. Is it the reason for the non-even distribution of bright fringes?

Moreover, for diffraction grating, should the bright fringes on each side also be non-evenly distributed?

• Both phenomena are all about allowable values of the transverse momentum. Consider a diffraction grating vs an infinite-slit arrangement. – Jon Custer May 29 '19 at 13:42
• Every slit pattern begins with light diffracting around the edges of the slits. The best example is a single edge diffraction pattern. You can easily derive any slit pattern as I show in "Single Edge Certainty" at billalsept.com – Bill Alsept Jan 6 at 17:33

The centre of the bright fringes that you see using a diffraction grating are in fact in exactly the same position as those produced by two slits with the same separation as that between adjacent slits when using a diffraction grating.

Given that the grating equation for the n$$^{\rm th}$$ maximum is usually written as $$n\lambda = d \sin \theta_{\rm n}$$ and it the same for the double slit you can say that the fringes are not equally spaced.

However for the normal double slit arrangement the angle $$\theta_{\rm n}$$ is small and so the approximation $$\sin \theta_{\rm n} \approx \theta_{\rm n}$$ can be used.
So $$y_{\rm n} \approx D \,\theta_{\rm n} = \frac{n \lambda\,D}{d} \Rightarrow y_{\rm n+1} -y_{\rm n} = \Delta y = \frac{(n+1) \lambda\,D}{d} - \frac{n\,\lambda\,D}{d} = \frac{\lambda\,D}{d}$$

This results in fringes which are observed to be equally spaced.

The advantage of using a diffraction grating is that the bright fringes are narrow and much brighter than those from a two slit arrangement as explained here.

The width of a slits controls the diffraction envelope ie modulate the intensity of the interference fringes.

• In double slit arrangement, the small angle approximation can be used. Does that mean the whole pattern span over only small range of 𝜃? but you said 𝑛𝜆=𝑑sin𝜃n can also be used in double slit arrangement. So, there will be fringes occurred at larger 𝜃 such that small angle approximation cannot be used. Does it mean the fringes occurred at larger 𝜃 are not evenly spaced? – phyphyphy May 30 '19 at 9:42
• @phyphyphy Usually because of potential visibility problems the double slit pattern is over a small range of small values of $\theta$. If you did observe the fringes at large angles of $\theta$ then they would not be equally spaced as per the diffraction grating. – Farcher May 30 '19 at 17:30