Complete Question
The complete question is shown on the first uploaded image
Answer:
The slit width [tex]a = \frac{2L \lambda}{W}[/tex]
Explanation:
Assuming the unit on the graph is cm
Given that the slit to screen distance is D = 200 cm = 20 000 m
The wavelength [tex]\lambda[/tex] = 633 nm = [tex]633*10^{-9}m[/tex]
slit width a = ?
The width of the spot that is the width of the peak from the graph is
W = 1.6 × 2 = 3.2 cm
Where the 1.6 is the distance from 0 to the right end point of the peak
The change in y i.e [tex]\Delta y[/tex] has a formula
[tex]\Delta y[/tex] = Ltanθ
An the width of the spot is 2 × [tex]\Delta y[/tex]
W = 2Ltanθ
Applying this formula qsinθ = m[tex]\lambda[/tex]
where m = 1 because we a focused on the first zeros ,using small angle approximation we have y
[tex]a\theta = (1) \lambda[/tex]
[tex]\theta = \frac{\lambda}{a}[/tex]
Substituting this into W = 2ltanθ
Using small angle approximation
W = 2ltanθ = 2Lθ
[tex]W = 2L\frac{\lambda}{a}[/tex]
[tex]a = \frac{2L \lambda}{W}[/tex] and this is the slit width
