Problem 27.37

27.37. a)
Assume a width of the middle finger of approximately 2 cm. Then it acts as the spacing in a two slit grating. The condition for constructive interference is given by
$d \sin \theta = m \lambda$
The first maximum would obviously be the central maximum. The second one is given by
$(.02 m) \sin \theta_{1} = 600 \times 10^{-9}$
Here I have chosen the wavelength of visible light to be about 600 nm. So, we then find that
$\theta_{1} \simeq .001{}^{\circ}$
Which is quite small.

b)
If I choose the angle to be say, $20{}^{\circ}$, then we would need EM radiation on the order of
$\lambda = (.02 m) \sin 20{}^{\circ}$
$\lambda \simeq 7 mm$
This corresponds to the microwave portion of the EM spectrum.