Half ( 50\% ) of the X-rays emitted from a Coolidge tube are able...

When the potential difference between the target and the filament is increased, the kinetic energy of the striking electrons increases.

This results in the emission of X-rays with higher maximum energy and shorter wavelength, as E = eV = \dfrac{hc}{\lambda_\min}.

Higher energy X-rays have greater penetrating power, meaning their absorption coefficient $\mu$ decreases.

The intensity of X-rays after passing through a thickness $x$ is given by $I = I_{0} e^{-\mu x}$.

For $50\%$ transmission, $I = \dfrac{I_{0}}{2}$, which gives the half-value thickness $x = \dfrac{\ln 2}{\mu}$.

Since the absorption coefficient $\mu$ decreases with an increase in X-ray energy, the required thickness $x$ to allow $50\%$ of the X-rays to pass through will increase.

Therefore, the new thickness required will be $> 0.1 \text{ mm}$.