Bright Lenses and Optical Depth

In gravitational lensing, the concept of optical depth assumes the lens is dark. Several microlensing detections have now been made where the lens may be bright. Relations are developed between apparent and absolute optical depth in the regime of the apparent and absolute brightness of the lens. An apparent optical depth through bright lenses is always less than the true, absolute optical depth. The greater the intrinsic brightness of the lens, the more likely it will be found nearer the source. Subject headings: gravitational lensing – dark matter