Refraction is the change in direction of a wave.
Diffraction is the bending of a wave around a barrier.
I added individual steps for clarity. Note that g must be positive if the solution is to be real.

Let me know if you have any questions.
Answer:
10.2 m
Explanation:
The position of the dark fringes (destructive interference) formed on a distant screen in the interference pattern produced by diffraction from a single slit are given by the formula:

where
y is the position of the m-th minimum
m is the order of the minimum
D is the distance of the screen from the slit
d is the width of the slit
is the wavelength of the light used
In this problem we have:
is the wavelength of the light
is the width of the slit
m = 13 is the order of the minimum
is the distance of the 13th dark fringe from the central maximum
Solving for D, we find the distance of the screen from the slit:

Answer:
The Earth's magnetism is generated in the core, which is composed of iron that is constantly churning
Explanation:
Magnetic fields are produced by charges in motion, therefore by currents.
The outer core of the Earth consists mainly of melted iron that is in constant motion. This iron in motion actually acts as a giant current, and therefore it is responsible for the creation of the Earth's magnetic field.
The magnetic field of the Earth is very weak, in fact its magnitude is on average between 25 and 65 microtesla (for comparison, normal magnets can even produce magnetic fields of a few millitesla).
However, its role is very important for the Earth: in fact, it provides a shield that blocks most of the harmful radiation coming from the Sun.