Homework help w/ youngs slit problems

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The discussion focuses on two physics problems related to interference patterns. The first problem involves calculating the total width of the central bright fringe in a two-slit experiment, with attempts yielding incorrect answers. The second problem addresses the width of a single slit based on the distance between dark fringes in a diffraction pattern, with the participant expressing confusion about the approach. The need for step-by-step guidance is emphasized to identify mistakes in the calculations. Clear explanations and problem-solving strategies are sought to resolve these issues effectively.
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I have a couple problems that I'm just not getting. Can someone help me out with these?


Problem 1

Homework Statement


A two-slit pattern is viewed on a screen 1.12m from the slits. If the two fifth-order minima are 78.5cm apart, what is the total width of the central bright fringe.

Attempts
I have gotten an array of answers, none of which are right.

4.677cm
8.673cm
and 3.014 cm



Problem 2

Homework Statement


A single slit is illuminated with 649nm light, and the resulting diffraction pattern is viewed on a screen 2.39m away. If the linear distance between the first and second dark fringes of the patter is 10.2cm, what is the width of the slit?

Attempts
nothing that came out right or making sense...
 
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Let's see what steps you took. There's no other way to spot your mistake.
 
the second one i feel like i just guessed on, i really didnt have much of a clue as to even where to start... give me a second and ill type up my work for the first.
 

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