Respuesta :
Answer:
y ’= y / 2
thus when the slit width is doubled the pattern width is halved
Explanation:
The diffraction of a slit is given by the expressions
     a sin θ = m λ
where a is the width of the slit, λ is the wavelength and m is an integer that determines the order of diffraction.
     sin θ = m λ / a
If this equation
     a ’= 2 a
we substitute
     2 a sin θ'= m λ
     sin θ'= (m λ / a)  1/2
     sin θ ’= sin θ / 2
     Â
We can use trigonometry to find the width
     tan θ = y / L
as the angle is small
     tan θ = sin θ / cos θ = sin θ
     sin θ = y / L Â
    Â
we substitute
    y ’/ L = y/L  1/2
    y ’= y / 2
thus when the slit width is doubled the pattern width is halved
