$(10$ marks$)$ Two narrow slits separated by $0\mathrm{.}1$ mm are illuminated by a laser and an interference pattern is formed on a viewing screen $2$ m away. On the screen, the distance between the central beam and the second intensity maximum is measured to be $1\mathrm{.}6$ cm $.$

a$)$ What is the wavelength of the light?

b$)$ What is the separation on the screen between consecutive dark fringes?

c$)$ A thin piece of glass