Answer:
a
The number of fringe is z = 3 fringes
b
The ratio is [tex]I = 0.2545I_o[/tex]
Explanation:
a
From the question we are told that
The wavelength is [tex]\lambda = 600 nm[/tex]
The distance between the slit is [tex]d = 0.117mm = 0.117 *10^{-3} m[/tex]
The width of the slit is [tex]a = 35.7 \mu m = 35.7 *10^{-6}m[/tex]
let z be the number of fringes that appear between the first diffraction-envelope minima to either side of the central maximum in a double-slit pattern is and this mathematically represented as
[tex]z = \frac{d}{a}[/tex]
Substituting values
[tex]z = \frac{0.117*10^{-3}}{35.7 *10^{-6}}[/tex]
z = 3 fringes
b
From the question we are told that the order of the bright fringe is n = 3
Generally the intensity of a pattern is mathematically represented as
[tex]I = I_o cos^2 [\frac{\pi d sin \theta}{\lambda} ][\frac{sin (\pi a sin \frac{\theta}{\lambda } )}{\pi a sin \frac{\theta}{\lambda} } ][/tex]
Where [tex]I_o[/tex] is the intensity of the central fringe
And Generally [tex]sin \theta = \frac{n \lambda }{d}[/tex]
[tex]I = I_o co^2 [ \frac{\pi (\frac{n \lambda}{d} )}{\lambda} ] [\frac{\frac{sin (\pi a (\frac{n \lambda}{d} ))}{\lambda} }{\frac{\pi a (\frac{n \lambda}{d} )}{\lambda} } ][/tex]
[tex]I = I_o cos^2 (n \pi)[\frac{\frac{sin(\pi a (\frac{n \lambda}{d} ))}{\lambda} )}{ \frac{ \pi a (\frac{n \lambda }{d} )}{\lambda} } ][/tex]
[tex]I = I_o cos^2 (3 \pi) [\frac{sin (\frac{3 \pi }{6} )}{\frac{3 \pi}{6} } ][/tex]
[tex]I = I_o (1)(0.2545)[/tex]
[tex]I = 0.2545I_o[/tex]
