Double slits are separated by 866 μ m and are distance L = 3.27 m from a screen

Question

Double slits are separated by 866 μm and are distance L = 3.27 m from a screen.
A monochromatic electromagnetic beam falls on the double slits, creating a diffraction pattern on the screen: the first minimum is 3.06 mm from the center of the central maximum.
i. Find the wavelength of this wave: nm
ii. Find the frequency of this wave: Hz
iii. For this beam: find the distance between the central maximum and the 267th maximum.
iv. Suppose the distance between the slits decreases at dd/dt = -28.8 μm/s, while λ and L remain constant. Find the rate at which the distance between the central and first maxima is changing at the instant d = 3.41 μm.
dx/dt = cm/s
v. Suppose a different monochromatic electromagnetic beam is used with the original slits, and now the second minimum falls where the original beam produced its first maximum. Find the wavelength of this new beam: λ = nm

Explanation / Answer

(iii). The central maximum is at 0, so you just need to find the distance of the 267th maximum, by y = (mlambda L/d) so y = (267)(your answer for part i)(3.27m)/866 ?m.

= m

(iv) so first the equation is (d = mlambda L/y) so plug in 3.41?m for d and find y. Then you find the derivative of that equation (rac{d?}{dt} = -mlambda L y^(-2) rac{d?}{dy})

thats supposed to say y^-2. Then you know m = 1, you know y, lambda and L are the same, and you are given d/dt. Just plug in the rest: -28.8 ? m/s = -(1)(lambda)(3.27m)*y^-2*(d/dy).

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