Question

Find the angle between the first minima for the two sodium vapor lines, which have wavelengths of 589.1 and 589.6 nm, when they fall upon a single slit of width 2.40 µm.

Answer 1

The angle between the first minima for two sodium vapor lines can be calculated using the formula θ = λ / w, where θ is the angle, λ is the wavelength of light, and w is the slit width. Using this formula, the angle for the sodium vapor lines with wavelengths of 589.1 nm and 589.6 nm is approximately 0.244 radians.

Step-by-step explanation:

The angle between the first minima for two sodium vapor lines can be determined using the concept of diffraction. The formula for calculating the angle is given by:

θ = λ / w

Where θ is the angle, λ is the wavelength of light, and w is the slit width.

Using this formula, we can find the angle for each of the sodium vapor lines:

For λ = 589.1 nm:

θ = (589.1 x 10^-9 m) / (2.40 x 10^-6 m)

θ ≈ 0.244 radians

For λ = 589.6 nm:

θ = (589.6 x 10^-9 m) / (2.40 x 10^-6 m)

θ ≈ 0.246 radians

Therefore, the angle between the first minima for the two sodium vapor lines is approximately 0.244 radians.

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