Question

Monochromatic light falls on two very narrow slits 0.048 mm apart. successive fringes on a screen 5.00 m away are 6.5 cm apart near the center of the pattern. determine the frequency of the light.

Answer 1

In a double-slit interference experiment, the distance y of the maximum of order m from the center of the observed interference pattern on the screen is
$y= \frac{m \lambda D}{d}$
where D=5.00 m is the distance of the screen from the slits, and 
$d=0.048 mm=0.048 \cdot 10^{-3}m$ is the distance between the two slits.
The fringes on the screen are 6.5 cm=0.065 m apart from each other, this means that the first maximum (m=1) is located at y=0.065 m from the center of the pattern.
Therefore, from the previous formula we can find the wavelength of the light:
$\lambda = \frac{yd}{mD}= \frac{(0.065 m)(0.048 \cdot 10^{-3}m)}{(1)(5.00 m)}= 6.24 \cdot 10^{-7}m$

And from the relationship between frequency and wavelength, $c=\lambda f$, we can find the frequency of the light:
$f= \frac{c}{\lambda}= \frac{3 \cdot 10^8 m/s}{6.24 \cdot 10^{-7}m}=4.81 \cdot 10^{14}Hz$