Answer:
The thickness is [tex]\Delta y = 2.4 *10^{-6} \ m[/tex]
Explanation:
From the question we are told that
The wavelength is [tex]\lambda = 480 \ nm = 480*10^{-9} \ m[/tex]
The first order of the dark fringe is [tex]m_1 = 16[/tex]
The second order of dark fringe considered is [tex]m_2 = 6[/tex]
Generally the condition for destructive interference is mathematically represented as
[tex]y = \frac{m \lambda}{2}[/tex]
Here y is the path difference between the central maxima(i.e the origin) and any dark fringe
So the path difference between the 16th dark fringe and the 6th dark fringe is mathematically represented as
[tex]y_1 - y_2 = \Delta y = \frac{m_1 \lambda}{2} - \frac{m_2 \lambda}{2}[/tex]
=> [tex]y_1 - y_2 = \Delta y = \frac{16 *480*10^{-9}}{2} - \frac{6 *480*10^{-9}}{2}[/tex]
=> [tex]y_1 - y_2 = \Delta y = 5 (480*10^{-9})[/tex]
=> [tex]\Delta y = 2.4 *10^{-6} \ m[/tex]
