Answer:
the separation of the interference maxima is directly proportional to the wavelength
the greatest separation must be obtained for the red light of
λ = 700
Explanation:
The double slit interference experiment is explained for the constructive interference case by the expression
d sin θ = m λ
where d is the separation between the slits, θ at the angle of separation of the different maxima, λ the wavelength and m the order of interference.
In these experiments the angles are always very small, so if the observation screen is at a large distance and y is the distance between the maximums, we can use trigonometry
tan θ = y / L
as the angle is small we can also use
tan θ = sin θ / cos θ = sin θ
when substituting we find
sin θ = y / L
the contributory interference equation remains
d y / L = m λ
y = m (L / d) λ
the quantity in parentheses is constant, so the variation in the separation of the interference maxima is directly proportional to the wavelength
by which the greatest separation must be obtained for the red light of
λ = 700
