Question
E6. For the same conditions described in exercise 5, at what
distance from the center of the screen will the fourth dark
fringe appear?
distance from the center of the screen will the fourth dark
fringe appear?
Ask by Frazier Montgomery. in the United States
Jan 23,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
To find the distance from the center of the screen where the fourth dark fringe appears, use the formula:
Where:
-
= distance to the dark fringe -
for the fourth fringe -
= wavelength -
= distance from slits to screen -
= slit separation
Plug in the known values and calculate
to find the exact distance.
Solution

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The Deep Dive
To find the distance from the center of the screen where the fourth dark fringe appears in a double-slit interference pattern, you can use the formula for dark fringes, which is:
Here,
represents the distance of the m-th dark fringe from the center,
is the wavelength of light,
is the distance to the screen from the double slits,
is the distance between the slits, and
is the order of the dark fringe (0, 1, 2,…).
For the fourth dark fringe,
(since we start counting from 0). Simply plug in the values for
,
, and
to find
.
And voila! You’ve determined the position of the fourth dark fringe!