# Why is titanium dioxide transparent for visible light but not for UV?

I wonder the reason for TiO2 thin films to be transparent for visible light but not for UV. I made a quick search and I found that it is due to the band gap of TiO2. It absorbs UV light but not visible light. I imagine this occurs because of the different wavelengths of these two types of radiation. But what is the relation between the wavelength of a certain type of radiation and the width of the band gap a semiconducting material? And how does this effect its optical properties?

• I once visited a lab where they were showing a little experiment. They gave us a silicon wafer (monocrystalline) and a piece of glass. They had set a UV camera connected to a screen. When I put the glass between me and the camera my face didn't appear on the screen (even though I was able to see it with my eyes). When I tried the same with the silicon wafer I didn't see with my eyes but my face appeared on the screen. Silicon is also transparent for UVs and not for visible light. Mar 27, 2014 at 10:03

The energy per photon of light with wavelegth $\lambda$ is given by:
$$E = \frac{hc}{\lambda}$$
$$\lambda \approx \frac{hc}{\Delta E}$$
where $\Delta E$ is the band gap. I've used the approximately equal sign because band gaps are rarely sharp and the light absorbtion will increase over a wavelength range of around the cutoff wavelength. If you want to establish the band gap accurately you'd use a Tauc plot.