Relief, simply speaking, is the contrast at the edge of a particle as a result of differences in the refractive index between the particle and the mounting medium. John Delly provides a more detailed definition in his book, ESSENTIALS OF POLARIZED LIGHT MICROSCOPY AND ANCILLARY TECHNIQUES. His definition is "Contrast between a specimen and its surroundings (typically mounting media) due to the difference between their refractive indices. The greater the numerical difference in refractive indices, the stronger the relief. Expressed as positive or negative; high, medium, or low."

The first image shows a glass fiber from an office ceiling acoustic tile. The refractive index of the glass fiber is about 1.520. The relief is moderate. The sign cannot be determined, positive or negative, from this image. If it were negative, refractive index lower than the mounting medium, then the fiber would become dark when the stage is lowered (bright Becke line out). If it were positive, refractive index higher than the mounting medium, then the fiber would become bright when the stage is lowered (bright Becke line in).

This image shows a glass fiber (lowere left) and a silica phytolith (upper right) with oblique illumination. The light is coming in from the right. The silica phytolith has a lower refractive index, relief is negative, and so is bright on the right. The glass fiber has a higher refractive index, relief is positive, and is dark on the right side. With oblique illumination the relative refractive index can be determined without having to defocus the particle.

Calcite has an omega refractive index of 1.658 or higher (in this case 1.669) and an epsilon prime refractive index in this orientation of about 1.550. The first image shows the relief created when a linear polarizer is oriented to show epsilon prime. The refractive index difference is 0.114. The result is high relief. The second image is with the crystal rotated 90 degrees, showing the omega refractive index. The difference is 0.005 refractive index units. The result is low relief. In this position, lowering the stage results in a orange Becke' line moving into the particle and an blue Becke' line moving out, as shown in the third image. If Oblique illumination is used the dispersion staining colors are evident on oposite sides of the crystal.

The optical glasses have a refractive index of 1.64, 1.66, and 1.67. The first image shows the calcite crystal in high relief and the 1.67 refractive index glass in low relief. The 1.66 refractive index glass is invisible. With oblique illumination, the second image, the optical glasses show dispersion staining colors.

The first image shows the olivine (upper left) and quartz (lower center) in slightly off crossed polarized light.
The second image is taken with oblique illumination and a single linear polarizing filter oriented parallel to the high refractive index of the olivine particle. The quartz is showing high negative relief. It is bright on the side of the light source and dark on the other side. That indicates that the refractive indices of the quartz (1.544 and 1.553) are well below 1.664. The high refractive index of the olivine particle is about 1.668, based on the dispersion colors shown.
The third image shows the particles with the linear polarizer rotated 90 degrees. The relief of the quartz particle has not changed. The olivine particle is now showing its low refractive index of about 1.656. It is now showing low negative relief because its refractive index in this position is slightly lower than the 1.664 of the mounting medium.