No single equation correlating all the three quantities was reported in literature. However, the three parameters are indiectly related as:

R= (n-1) ^2+k^2/ (n+1) ^2+k^2. ------ [i].

Here R is reflectivity and n is refractive index and k is the extinction coefficient.

R+A+T=1 --------- [ii] and

k= α. λ/4π ----- [iii]

α. (optical absorption coefficient) = 2.303A/t--- (b) – [iv].

A is absorbance and t is thickness of film.

Also,

α = (h. ν -Eg) ^1/2 -----[iv].

Eg is band gap.

See, for example, paper http://www.sciencedirect.com/science/article/pii/S0030401811000125

No single equation correlating all the three quantities was reported in literature. However, the three parameters are indiectly related as:

R= (n-1) ^2+k^2/ (n+1) ^2+k^2. ------ [i].

Here R is reflectivity and n is refractive index and k is the extinction coefficient.

R+A+T=1 --------- [ii] and

k= α. λ/4π ----- [iii]

α. (optical absorption coefficient) = 2.303A/t--- (b) – [iv].

A is absorbance and t is thickness of film.

Also,

α = (h. ν -Eg) ^1/2 -----[iv].

Eg is band gap.

Statement answers reveals that increase of thickness will cause reduction of bandgap due to increase of grain crystal size.

Manohar Sehgal has got all the key equations covered. What I would add is that while the refractive index and thickness do depend on R&T or ellipsometry data via clear equations, the band gap is more tricky. There are several models that correlate alpha and Eg for different types of materials with different band structures.

Thks.Dr. Manuel Schnabel for your very kindly sparing your time for my way of correlating the said parameters.Yes; I agree with your self regarding the band gap calculation,but the given relation may serve the best in most cases.