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7.87° is the first-order maximum for 550 nm.

What is diffraction?

  • Diffraction is the spreading of waves in the presence of obstacles. Diffraction occurs with sound, electromagnetic radiation such as light, X-rays, and gamma rays, and very small moving particles with wavelike properties such as atoms, neutrons, and electrons.
  • The locations of the interference fringes are given by the equation d sin θ = m λ d sin θ = m λ.

Using diffraction equations,

d = 0.01/Number of lines, where 0.01 m = 1 cm and d = line spacing

Therefore,

d = 0.01/2070 = 4*10^-6 m

Similarly,

d x Sin X = m x Y;

When X = Angle

m = order = 1

Y = wavelength = 550 nm =550*10^-9 m

By substituting;

Sin X = mY / d = (1*550*10^-9)/(4*10^-6) = 0.1375

X = Sin⁻¹(0.1375) = 5.97°

As a result, the first-order maximum for 550 nm will be 7.87°.

To learn more about diffraction refer to :

https://brainly.com/question/8645206

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