Hi there,

For estimation I can recommend a simple calculator that only requires wavelength input: http://www.instanano.com/characterization/theoretical/uv-vis-spectroscopy-band-gap-calculation/  

As to the formulas, equation 2 comes from Lambert-Beer's law and can be applied not only for thin films.

Both equations are valid to find the band gap of thin films or nanoparticle dispersions or solid. Another equation is also useful to found the  band gap of same.

(ahv)=A(hv-Eg)1/2

where,a is the absorption coefficient,h is Planck's constant,nis the frequency of radiation,A is an appropriate constant,Eg is the bandgap.

For experimental evaluation of the forbidden band gap is necessary to determine the absorption edge. The absorption edge can be determined by extrapolation of the linear dependence of the reflection coefficient curve to its intersection with the x-axis (wavelength). The intersection point determines the absorption edge

2.303=ln10, so the difference stems from two different definitions of your alpha...and the first alpha is usually an epsilon... ;-)

Addition to Michails answer: depending on the signal (scattering) the range above the absorbance of the particle have also to be fitted by a linear equation. Then the intersection between both linear equations can be defined to be the onset of absorbance. I hope that you understood the onset is the minimal distance in between the highest occupied band and the lowest non-occupied band. It is not a orbital it's a band. Hence that means if you use more energy than the bandgab more electrons can be excited. Hence the bandgab is not the maximum. For orbital orbital transitions it's not per se the minimal distance. You have to consider the frank canton princip. To fully understand this you should search for analysis of I2 Uv-vis specta.