Answer:
[tex]\alpha = 4.742*10^{-5}/ \°C[/tex]
Explanation:
[tex]n= 1.750[/tex]
[tex]\lambda = 583.5nm[/tex]
In this way we understand that the condition for destructive interference is
[tex]2t = \frac{m \lamba}{n}[/tex]
The smallest non zero thickness is,
[tex]t= \frac{\lambda}{2n}[/tex]
At [tex]22.2\° C[/tex]
[tex]t_0 = \frac{583.5nm}{2(1.750)}[/tex]
[tex]t_0 = 166.7nm[/tex]
At [tex]174\° C[/tex]
[tex]t= \frac{587.5nm}{2(1.750)}[/tex]
[tex]t= 167.9nm[/tex]
[tex]t= t_0 (1+\alpha \Delta T)[/tex]
The coefficient of linear expansion is
[tex]\alpha = \frac{t-t_0}{t_0 \Delta T}[/tex]
[tex]\alpha = \frac{167.9nm-166.7}{166.7(174\° - 22.2\°)}[/tex]
[tex]\alpha = 0.00004742/ \°CC[/tex]
[tex]\alpha = 4.742*10^{-5}/ \°C[/tex]