Young's double slit experiment decreasing distance

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Decreasing the distance between slits in Young's double slit experiment affects the angle of the interference maxima, as described by the equation d sin(theta) = m*lambda. When the slit separation (d) is reduced while keeping the wavelength (lambda) constant, the angle (theta) for the maxima increases. This relationship shows that smaller slit separations lead to wider spacing of the interference patterns on the screen. Additionally, the condition for valid angles requires that the ratio (m*lambda) / d remains within the bounds of -1 to 1. Understanding these dynamics is crucial for analyzing the behavior of light in interference experiments.
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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
 
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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
 

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