Answer:
The ratio is [tex]k:d = 1 : 5[/tex]
Explanation:
From the question we are told that
The first minimum of the single slit pattern falls on the fifth maximum of the double slit pattern.
Generally the condition for constructive interference for as single slit is
[tex]ksin(\theta) = n\lambda[/tex]
Here k is the width of the slit and n is the order of the fringe and for single slit n = 1 (cause we are considering the first maxima)
Generally the condition for constructive interference for as double slit is
[tex]dsin\theta = m\lambda[/tex]
Here d is the separation between the slit and m is the order of the fringe and for double slit m = 5 (cause we are considering the first maxima)
=> [tex]dsin\theta = 5\lambda[/tex]
So
[tex]\frac{ksin(\theta)}{dsin(\theta)} = \frac{\lambda}{5\lambda}[/tex]
=> [tex]\frac{k }{d} = \frac{1}{5}[/tex]
So
[tex]k:d = 1 : 5[/tex]
