Consider point B, the first maximum to the left of the center of the screen. Suppose that the two slits are separated by 0.2 mm, that the screen is 1.2 m away from the slits, and that the distance from the center of the pattern (point C) to point B is 3.6 mm. Use this information to determine the wavelength of the light. Describe any approximations you make in answering this question.

λ = 6 10⁻⁷ m

Explanation:

This problem is a double slit interference spectrum where bright maxima are described by constructive interference.

             d sin θ = m λ

Where d is the gap  of the slits (d = 0.2 10⁻³ m), m is the maximum interference and λ is the wavelength

We used trigonometry to find the angle

         tan θ = y / x

Since the angles in these experiments are very small we use

            tan θ = sin θ / cos θ = sin θ

            sin θ = y / x

We substitute

          d y / x = m λ

          λ = d y / m x

In this case the first maximum is m = 1

We substitute

            λ = 0.2  10⁻³  3.6 10⁻³ / (1   1.2)

            λ = 6 10⁻⁷ m

The approximation made in this problem is that since the angles are small we approximate the tangent to the sine

see earlier