Final answer:
The quantity not needed is (D) the angle formed by the paths from the slits to the center band and the first bright band; the small angle approximation allows us to calculate wavelength using the distance between the slits, the screen, and the central and first bright bands.
Step-by-step explanation:
To calculate the wavelength from a double-slit experiment using the small angle simplification, we typically need certain pieces of information. However, you do not need the actual angle formed by the paths from the slits to the central and first bright band if you are given the distance between the center bright band and the first bright band, and the screen is a large distance away compared to the distance between the slits. This is because under the small angle approximation, the sine of the angle can be replaced with the opposite over hypotenuse of the triangle formed by the distance between the bands on the screen and the distance from the slits to the screen.
Therefore, the quantities normally needed for the calculation are the distance between the slits (d), the distance from the slits to the screen (L), and the distance between the center bright band and the first bright band (y). With these, we can use the formula for the path difference ΔL = d sin θ = mλ (where m is the order of the bright fringe) and the small angle approximation sin θ ≈ θ ≈ y/L. The unnecessary quantity is (D) the angle formed by the paths from the slits to the center band and the first bright band, because it is not directly used in calculations when making the small angle approximation.