Answer:
The value is [tex]a = 0.000137 \ m[/tex]
Explanation:
From the question we are told that
The distance from the screen is D = 1.30 m
The wavelength of the light source is [tex]\lambda = 560 \ nm = 560 *10^{-9} \ m[/tex]
The path difference is mathematically represented as [tex]y = 5.30 *10^{-3} \ m[/tex]
Generally the path difference is mathematically represented as
[tex]y = \frac{m * D * \lambda }{a}[/tex]
Here m is 1 given that we are considering the first dark fringe
So
[tex]a = \frac{ m * \lambda * D}{y}[/tex]
=> [tex]a = \frac{1 * 560 *10^{-9 } * 1.30 }{ 5.30 *10^{-3}}[/tex]
=> [tex]a = \frac{1 8 560 *10^{-9 } * 1.30 }{ 5.30 *10^{-3}}[/tex]
=> [tex]a = 0.000137 \ m[/tex]
