Answer:0.024 mm
Explanation:
Given
Fringe shifts by an amount to 30 dark bands i.e. [tex]m=30[/tex]
Wavelength [tex]\lambda =480 nm[/tex]
refractive index of mica [tex]n_2=1.6[/tex]
refractive index of air [tex]n_1=1[/tex]
Phase difference is given by
[tex]m=\frac{t\left [ n_2-n_1\right ]}{\lambda }[/tex]
[tex]30=\frac{t\left [ 1.6-1\right ]}{480\times 10^{-9}}[/tex]
[tex]t=\frac{30\times 480\times 10^{-9}}{1.6-1}[/tex]
[tex]t=0.024\ mm[/tex]