Answer:
The value is [tex]t = 9.861 *10^{-8} \ m[/tex]
Explanation:
From the question we are told that
The refractive index of glass is [tex]n_{glass} = 1.5[/tex]
The wavelength is [tex]\lambda = 710 nm = \frac{710}{1 * 10^9} = 710*10^{-9} \ m[/tex]
The refractive index of oil is [tex]n_{oil} = 1.8[/tex]
Generally the condition for refractive index is mathematically represented as
[tex]2 * t = [m + \frac{1}{2} ] \frac{\lambda}{n_{oil}}[/tex]
Where t is the separation between two parallel plates of glass , now at minimum m which is the order of maxima produced is = 0
So
[tex]2 * t = [0 + \frac{1}{2} ] \frac{710 *10^{-9}}{1.8}[/tex]
[tex]t = 9.861 *10^{-8} \ m[/tex]