Answer:
a)Δy = 81.7mm
b)Δy = 32.7cm
Explanation:
To calculate the distance between any point of the interference pattern, simply use the trigonometric ratio of the tangent:
[tex]Tan \theta = \frac{y}{D}[/tex]
where D is the separation between the slits and the screen where the interference pattern is observed.
a) In this case:
Δy = |y1max (λ1) − y1max (λ2)|
Δy = [tex]|\frac{D\lambda _1}{d} - \frac{D\lambda _2}{d} |[/tex]
Δy = [tex]D |\frac{d/20}{d} - \frac{d/15}{d} |[/tex]
Δy = [tex]D |\frac{1}{20} - \frac{1}{15} |[/tex]
Δy = [tex]4.90 |\frac{1}{20}- \frac{1}{15} |[/tex]
Δy = 81.7mm
The separation between these maxima is 81.7 mm
b)
Δy = |y₂max (λ1) − y₂max (λ2)|
Δy = [tex]D|\frac{2(d/20)}{d} - \frac{5(d/15)}{2d} |[/tex]
Δy = [tex]4.90|\frac{1}{10} - \frac{1}{6} |[/tex]
Δy = 32.7cm
The separation between the maximum interference of the 2nd order (2nd maximum) of the pattern produced by the laser 1 and the minimum of the 2nd order (3rd minimum) of the pattern produced by the laser 2 is 32.7 cm.
