Answer: 0.0063π ( in radian)
θ = 1.14°( in degree)
Explanation: an interference experiment is defined by the formulae below
d* sin θ = mλ
d = distance between slits = 50um = 50*10^-6m
λ = wavelength of light = 500nm = 500 * 10^9m
m = order of fringe ( either bright or dark)
θ = between bright fringe
50 * 10^6 * sin θ = 2 * 500 * 10^9
sin θ = 2 * 500 * 10^9 / 50 * 10^6
sin θ = 1000 * 10^9 / 50 * 10^6
sin θ = 20 * 10³
sin θ = 0.02
θ = sin ^-1 ( 0.02)
θ = 1.14° ( in degree)
b) in radian.
Recall that 1π = 180° hence 1.14° is given below as
1.14° = π ×1.14/180
= 0.0063π
I. The angle of the m = 2 bright fringe in degrees is 1.15.
II. The angle of the m = 2 bright fringe in radians is 0.0201.
Given the following data:
To determine the angle of the m = 2 bright fringe in degrees, we would apply an interference experiment formula:
Mathematically, an interference experiment is given by the formula:
[tex]dsin\theta =m \lambda[/tex]
Where:
Making [tex]\theta[/tex] the subject of formula, we have:
[tex]\theta = sin^{-1}(\frac{m\lambda}{d} )[/tex]
Substituting the given parameters into the formula, we have;
[tex]\theta = sin^{-1}(\frac{2\times \; 5\times 10^{-7}}{5\times 10^{-5}} )\\\\\theta = sin^{-1}(\frac{10\times 10^{-7}}{5\times 10^{-5}} )\\\\\theta = sin^{-1}(0.02)\\\\\theta = 1.15[/tex]
Angle = 1.15°
Angle in radians:
[tex]1.15 \times \frac{\pi}{180} = 0.0201 \; rads[/tex]
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