Young's double slit experiment decreasing distance

[xswtxoj]

Main Question or Discussion Point

what the advantage of decreasing the distance between slits in a Young double slit experiment? i think to have the laser move closer to the screen

 

[buffordboy23]

Well, let's take a look. The maxima are given by the equation

d sin(theta) = m*lambda

where d is the slit separation, theta is the angle from the central axis to the maxima associated with the integers m, and lambda is the wavelength of the coherent light source.

We can rearrange this equation as

theta = arcsin[ (m*lambda) / d ]

Choose any m and keep lambda constant. Now vary the slit separation d. How does theta change with smaller and smaller values of d? It looks like a homework problem so I will let you tell me the answer. Also, note that the argument of arcsin requires

-1 <= (m*lambda) / d <= 1