Final answer:
The allowed values of mĮ for a given value of 1 can be found using the magnification equation, while the allowed values of mĮ for a given value of n can be determined by considering the interference pattern in single-slit diffraction. Examples in each case are provided.
Step-by-step explanation:
For a given value of 1, the allowed values of mĮ can be found by using the magnification equation, which relates the object distance (do), the image distance (di), and the magnification (m). It can be written as:
m = -di/do
The allowed values of mĮ for a given value of n can be found by considering the interference pattern produced by a single-slit diffraction. Destructive interference occurs when the path difference between the two interfering waves is an odd multiple of half the wavelength. In this case, the allowed values of mĮ would be the locations of destructive interference in the diffraction pattern.
A specific example for each case:
Example 1: For a given value of 1, let's say do = 20 cm and di = -10 cm. Substituting these values into the magnification equation gives:
m = -(-10 cm) / 20 cm = 0.5
Example 2: For a given value of n, let's say the wavelength is 600 nm and the distance between the screen and the single-slit is 1 m. Using the interference condition, we can find the allowed values of mĮ by computing the path difference and determining where destructive interference occurs.