We present a physics-based illumination estimation approach explicitly designed to handle natural images under ambient light. Existing physics-based color constancy methods are theoretically perfect but do not handle real-world images well because the majority of these methods assume a single illuminant. Therefore, specular pixels selected using existing methods produce estimated dichromatic lines that are thick or curvilinear in the presence of ambient light, thus generating significant errors. Based on the Phong reflection model, we show that a group of specular pixels on a uniformly colored object, although they are subject to intensity thresholding, produce a unique dichromatic line length depending on the geometry of each image path. Assuming that the longest dichromatic line is the most desirable when estimating the chromaticity of an illuminant, ambient-robust specular pixels are also found on the same path on which the longest dichromatic line segment is generated. Therefore, we propose a method to find the optimal image path in which the specular pixels produce the longest dichromatic line. Even though the number of collected specular pixels is reduced using the proposed method, they are proven to be more accurate when determining the illuminant chromaticity even in the existing methods. Experiments with an established benchmark data set and a self-produced image set find that the proposed method is better able to locate the illuminant chromaticity compared with the state-of-the-art color constancy methods.