Final answer:
The calculation of the first-order maximum angle for red light in a double slit experiment is unreasonable because the slit separation (400 nm) is less than the wavelength of light (700 nm), making a clear diffraction pattern impossible. The assumption of obtaining a first-order maximum under these conditions is inconsistent with required physical principles.
Step-by-step explanation:
First-Order Maximum Angle for Red Light in a Double Slit Experiment
To calculate the first-order maximum angle for red light in a double slit diffraction pattern, we can use the formula for double slit interference, which is d sin(\theta) = m\lambda, where d is the separation between the slits, \(\theta\) is the angle of the diffraction maximum, m is the order of the maximum, and the wavelength of the light.
In this situation, the wavelength of red light is 700 nm, the slit separation d is 400 nm, and we are looking for the first-order maximum, so m is 1. Plugging these values into the formula, we have:
400 nm * sin(\theta) = 1 * 700 nm
This equation has no real solution because the sine of an angle cannot be greater than 1, which highlights that there is something unreasonable with this problem setup.
Unreasonable Aspects of the Problem
The unreasonable aspect here is that the separation between the slits is smaller than the wavelength of the light used. Typically, for a clear diffraction pattern to form, the slit separation should be on the same order of magnitude as the wavelength or larger. When the slit separation is less than the wavelength, the light cannot be diffracted properly, and a well-defined interference pattern will not form.
Assumptions that are inconsistent include the assumption that a first-order maximum could exist when the slit separation is less than the wavelength of the light. This is inconsistent with the conditions necessary for double slit interference patterns.