Final answer:
To find the value of m20, we can use the equation d sin θ = mλ, where d is the distance between the slits, θ is the angle of the interference maximum, m is the order of the interference maximum, and λ is the wavelength of light.
Step-by-step explanation:
To find the value of m20, we can use the equation d sin θ = mλ, where d is the distance between the slits, θ is the angle of the interference maximum, m is the order of the interference maximum, and λ is the wavelength of light. From the given information, we know that mZN = 74°. Since the interference maximum occurs at an angle of 2.87° for m = 20, we can substitute these values into the equation to solve for m20.
d sin θ = mλ
Using the values d = 2.87°, θ = 2.87°, and mZN = 74°, we can rearrange the equation to solve for λ:
λ = (d sin θ) / mZN
Substituting the values into the equation, we have:
λ = (2.87° sin 2.87°) / 74°
Calculating this expression will give us the value of λ, and from that we can determine the value of m20 using the equation m = λ / d sin θ.