A monochromatic light falls on two narrow slits that are 4.50 um apart. The third destructive fringes which are 35° apart were formed at a screen 2m from the light source. The light source is 0.30 m from the slits. () Calculate Ym. (4 marks) Compute the wavelength of the light. (4 marks)​

 y = 1.19 m  and λ = 8.6036 10⁻⁷ m

Explanation:

This is a slit interference problem, the expression for destructive interference is

          d sin θ = m λ

indicate that for the angle of θ = 35º it is in the third order m = 3 and the separation of the slits is d = 4.50 10⁻⁶ m

          λ = d sin  θ / m

let's calculate

          λ = 4.50 10⁻⁶ sin 35  /3

          λ = 8.6036 10⁻⁷ m

for the separation distance from the central stripe, we use trigonometry

         tan θ= y / L

         y = L tan θ

the distance L is measured from the slits, it indicates that the light source is at x = 0.30 m from the slits

         L = 2 -0.30

         L = 1.70 m

let's calculate

        y = 1.70 tan 35

        y = 1.19 m

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