Final answer:
Missing orders in a double-slit diffraction pattern occur when conditions for interference maxima and diffraction minima coincide. By using the formulae for interference and diffraction related to the slit properties and light wavelength, one can deduce at which angles these missing orders will appear.
Step-by-step explanation:
The question posed relates to the phenomenon of missing orders in a double-slit Fraunhofer diffraction pattern. Missing orders in the context of a double-slit experiment occur when an interference maximum coincides with a diffraction minimum. Given that the slit widths are 0.16 mm and their separation is 0.96 mm, to deduce missing orders, one must apply the principle of superposition for both diffraction and interference effects.
In a double-slit experiment, the condition for maxima in the interference pattern is given by d sin(θ) = mλ, where d is the separation of slits, m is the order of the maximum, θ is the angle of deviation, and λ is the wavelength of light used. For diffraction minima, the condition is a sin(θ) = (n + 1/2)λ, where a is the width of the slits, and n is the order of the minimum.
If interference maximum coincides with diffraction minimum, their conditions are equal, leading to (a/d)(m) = (n + 1/2), where m/n are integers. By finding combinations that satisfy this condition for given a, d, and λ, one can identify the missing orders. The use of the ratio (width of slits)/(separation between slits) and applied conditions can determine at which angles these coincidences, and thus the missing orders, occur within a diffraction pattern.