Previous studies have shown that glass displays extracted from mobile phones are suitable as emergency dosimeters in case of an accidental radiation overexposure using the thermoluminescence (TL) method. So far these studies have focused only on recovering the absorbed dose to the material. However, dose in air or dose to the victim carrying the device might be significantly different. Therefore the aim of this work was to investigate photon energy dependence and angular response of glass display used in modern mobile phones. An over-response of about a factor of five is observed for low photon energies compared to the response to Cs-137 (662 keV) which is in reasonable agreement with calculated values mass energy-absorption coefficients of glass and air. Little variation in the energy dependence can be seen for glass displays coming from three different mobile phone models. The angular response for display glass is flat with regard to air kerma within the incident angle of ±60°, independent of the irradiation setup used (with a water phantom or with air kerma reference conditions). For incident angles of 90° the shielding effect of the mobile phones becomes important. With the dosimetric characterization of the photon energy and angular dependencies the absorbed dose in a glass display can be transferred to a reference air kerma dose and provides a useful option for retrospective accident dosimetry.