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

y = y₀ / 4

Step-by-step 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