Question

g If we decreased the wavelength by a factor of 2 and also increased the distance D by a factor of 2, the fringes on the screen would be...

Answer 1

Answer:

y = y₀ / 4

Explanation:

In a double slit experiment the constructive interference lines are given by

          d sin θ = m λ

if we use trigonometry

          tan θ = y / L

as in these experiments the angles are very small

          tan θ = sin θ /cos θ = sin θ

         

we substitute

         sin θ = y / L

          d y / L = m λ

let's use a subscript "o" for the initial values  

          I = m λ₀ L /d₀

They ask us to decrease the wavelength by 2

           λ =  λ₀ / 2

the distance in the slit is increased by a factor of two

         d = 2 d₀

we substitute

          2d₀  y/L = m  λ₀/2

          y = m  λ₀ L/d₀    ¼

          y = y₀ / 4