Double slits are separated by 866 μm 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.

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

iv)

d sinTheta = lamda

==> d x/L = lamda

==> x = L lamda/d

==> dx/dt = -L lamda/d^2 (dd/dt)

==> dx/dt = (-3.27*lamda/(3.41e-6*3.41e-6)) * (-28.8e-6)

==> dx/dt = 8099000 * lamda

input lamda to find dx/dt in m/s

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