Since the Sony SLT cameras do always expose the sensor to part of the light, through the translucent mirror, i was wondering if you should always put on the lens cap. For example taking a picture directly into the sun with open aperture can damage the sensor, so does putting the lens cap on make sense ? Or can the sensor only be harmed when turned on ? I couldn't find an answer through google.
The mechanical shutter is still between the translucent mirror and the sensor when the camera is turned off. Even if you select the option to use electronic first curtain with mechanical second curtain, which leaves the shutter open just as many cameras do to use Live View or record video, it doesn't leave the sensor unprotected when the camera is turned off. So the sensor is always somewhat protected from direct sunlight when the camera is turned off because a shutter curtain always covers the sensor when the camera is turned off.
Having said that, there are plenty of other parts of your Sony SLT camera that can be damaged by focused sunlight, so a camera should never be pointed at an angle that allows direct sunlight to enter the lens for an extended period of time. How quickly the damage can occur is highly variable depending on things such as the lens' focal length, the angle of the sun in the sky (more energy from the sun reaches the Earth's surface when it is high in the sky than when it is near the horizon), the focus setting of the lens, etc. With a 600mm telephoto lens aimed so the sun was just off the field of view of the sensor, but still inside the image circle it took about one minute to melt part of the inside of a Canon EOS 1Ds Mark III camera. The full article about how this happened during a lens flare test is at The Digital Picture.