Answer:
a.3.20m
b.0.45cm
Explanation:
a. Equation for minima is defined as: [tex]sin \theta=\frac{m\lambda}{\alpha}[/tex]
Given [tex]m=3[/tex],[tex]\lambda=6.33\times 10^-^7[/tex] and [tex]\alpha=0.00015[/tex]:
#Substitute our variable values in the minima equation to obtain [tex]\theta[/tex]:
[tex]\theta=sin^-^1 (\frac{3\times 6.33\times 10^-^7}{0.00015})\\\\\theta=0.01266rad[/tex]
#draw a triangle to find the relationship between [tex]\theta, y \[/tex] and [tex]L[/tex].
[tex]tan(\theta)=y/L[/tex] #where [tex]y=4.05cm[/tex]
[tex]L=y/tan(\theta)=3.20[/tex]
Hence the screen is 3.20m from the split.
b. To find the closest minima for green(the fourth min will give you the smallest distance)
#Like with a above, the minima equation will be defined as:
[tex]sin \theta=\frac{m\lambda}{\alpha}[/tex], where [tex]m=4[/tex] given that it's the minima with the smallest distance.
[tex]sin \theta=\frac{4\lambda}{\alpha}\\\theta=sin^-^1 (\frac{4\times 6.33\times 10^-^7}{0.00015})\\\\\theta=0.01688rad[/tex]
#we then use [tex]tan(\theta)=y/L[/tex] to calculate [tex]L[/tex]=4.5cm
Then from the equation subtract [tex]y_3[/tex] from [tex]y[/tex]:
[tex]4.50cm-4.05cm=0.45cm[/tex]
Hence, the distance [tex]\bigtriangleup y[/tex] is 0.45cm
