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A pair of narrow slits, separated by 1.8 mm, is illuminated by a monochromatic light source. light waves arrive at the two slits in phase, and a fringe pattern is observed on a screen 4.8 m from the slits. if there are 6.0 complete bright fringes per centimeter on the screen near the center of the pattern, what is the wavelength of the monochromatic light?

Respuesta :

Demiurgos
For the bright fringes to appear the difference in the path traveled must be multiple of the wavelength: 
[tex]dsin(\theta)=m\lambda[/tex]
Using approximation when y is much smaller than L:
[tex]sin(\theta)= \frac{y}{L}[/tex]
We get: 
[tex]y=\frac{m\lambda L}{d}[/tex]
Which means that distance between two bright fringes is: 
[tex] \Delta y= \frac{\lambda L }{d} [/tex]
We know that in our case the distance between two bright fringes is: 
[tex]\Delta y=\frac{1cm}{6}=0.166cm[/tex]
[tex]\lambda=\frac{\Delta y d}{L}=6.2475\cdot10^{-7}m=624.75nm[/tex]

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