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Two slits are illuminated by light of wavelength λ𝜆. The slits are spaced 1010 λ𝜆 apart. What is the angle, in radians, between the central maximum and the m=22 bright fringe? radians

Question

Two slits are illuminated by light of wavelength λ𝜆. The slits are spaced 1010 λ𝜆 apart. What is the angle, in radians, between the central maximum and the m=22 bright fringe? radians

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Solution

The angle θ between the central maximum and the m-th bright fringe in a double-slit experiment is given by the formula:

θ = arcsin(m * λ / d)

where:

  • m is the order of the fringe,
  • λ is the wavelength of the light, and
  • d is the distance between the slits.

In this case, m = 2, λ = λ (we'll keep it as λ since we don't know the specific wavelength), and d = 10λ.

Substituting these values into the formula, we get:

θ = arcsin(2 * λ / 10λ)

Simplifying the right side of the equation, we get:

θ = arcsin(2/10)

Therefore, the angle θ in radians between the central maximum and the m=2 bright fringe is:

θ = arcsin(0.2) radians.

This problem has been solved

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