Answer:
The angular separation is [tex]k = 0.8594^o[/tex]
Explanation:
From the question we are told that
The wavelength of the light is [tex]\lambda = 600 \ nm = 600*10^{-9} \ m[/tex]
The distance of separation between the slit is [tex]d = 0.080 \ mm = 0.080 *10^{-3} \ m[/tex]
The distance from the screen is
Generally the condition for constructive interference is mathematically represented as
[tex]d \ sin(\theta) = n \lambda[/tex]
=> [tex]\theta = sin ^{-1} [ \frac{n * \lambda }{ d } ][/tex]
here [tex]\theta[/tex] is the angular separation between the central maxima and one side of the first order maxima
given that we are considering the first order of maxima n = 1
=> [tex]\theta = sin ^{-1} [ \frac{1 * 600*10^{-9} }{ 2.0 } ][/tex]
=> [tex]\theta = sin ^{-1} [ 0.0075 ][/tex]
=> [tex]\theta = 0.4297^o[/tex]
So the angular separation of the two first order maxima is
[tex]k = 2 * \theta[/tex]
[tex]k = 2 * 0.4297[/tex]
[tex]k = 0.8594^o[/tex]
