Question

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.

Answer 1

λ = 6 10⁻⁷ m

Step-by-step 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