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Answer:
a) y = 2.4 x 10⁻³ m = 0.24 cm
b) y = 3.2 x 10⁻³ m = 0.32 cm
Explanation:
The formula of Young's Double Slit experiment will be used here:

where,
y = distance between dark spots = ?
λ = wavelength
L = distance of screen = 2 m
d = slit width = 4 x 10⁻⁴ m
a) FOR λ = 480 nm = 4.8 x 10⁻⁷ m:

<u>y = 2.4 x 10⁻³ m = 0.24 cm</u>
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a) FOR λ = 640 nm = 6.4 x 10⁻⁷ m:

<u>y = 3.2 x 10⁻³ m = 0.32 cm</u>
To solve this problem we will apply the laws of Mersenne. Mersenne's laws are laws describing the frequency of oscillation of a stretched string or monochord, useful in musical tuning and musical instrument construction. This law tells us that the velocity in a string is directly proportional to the root of the applied tension, and inversely proportional to the root of the linear density, that is,

Here,
v = Velocity
= Linear density (Mass per unit length)
T = Tension
Rearranging to find the Period we have that


As we know that speed is equivalent to displacement in a unit of time, we will have to



Therefore the tension is 5.54N
Answer:
The width of the central bright fringe on the screen is observed to be unchanged is 
Explanation:
To solve the problem it is necessary to apply the concepts related to interference from two sources. Destructive interference produces the dark fringes. Dark fringes in the diffraction pattern of a single slit are found at angles θ for which

Where,
w = width
wavelength
m is an integer, m = 1, 2, 3...
We here know that as
as w are constant, then

We need to find
, then

Replacing with our values:


Therefore the width of the central bright fringe on the screen is observed to be unchanged is 