Question

The largest and smallest slits in these experiments are 0.16mm and 0.04mm wide, respectively. The wavelength of the laser light is 650nm. How many wavelengths wide are these slits?

Answer 1

To solve this problem we will convert the values given to international units (meters) and then proceed to calculate the number of wavelengths through the division of the width over the wavelength. This is,

$\lambda = 650 nm =650 * 10^{-9} m$

$w_1 = 0.16 mm = 0.16 * 10^{-3} m$

$w_2 = 0.04 mm =0.04 * 10^{-3} m$

Now the number of wavelengths is the division between the total width over the wavelength therefore

First case,

$\frac{w_1}{\lambda} = \frac{ 0.16 * 10^{-3}}{650 * 10^{-9}} = 4062.5 * 10^6$

Second case,

$\frac{w_2}{\lambda} = \frac{0.04 * 10^{-3} }{650 * 10^{-9} } = 16250 * 10^6$