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Some options are available only in Advanced mode.

Refraction – Enables Refraction of the material.

Refraction Color – Specifies the refraction color. Note that the actual refraction color depends on the reflection color as well. Set the color to black to disable the refraction layer. For more information about refraction color, please see the Refraction Color Parameter example below.

IOR² – Specifies the index of refraction for the material, which describes the way light bends when crossing the material surface. A value of 1.0 means the light does not change direction. For more information, please see the Refraction IOR Parameter example below.

Refraction Glossiness² – Specifies the sharpness of refractions. A value of 1.0 produces perfect glass-like refraction; lower values produce blurry or glossy refractions. Use the Subdivs parameter below to control the quality of glossy refractions. For more information, please see the Refraction Glossiness Parameter example below.

Thin-Walled – Simulates single-surface transparent materials. When enabled and the Translucency mode is set to SSS, it simulates thin translucent surfaces such as soap bubble, leaves, curtains, etc. The SSS color defines the backside color, while the SSS amount controls the translucency effect. For more information, please see the Thin-Walled example below.

Translucency – Selects the algorithm for calculating translucency (also called sub-surface scattering).

None – No sub-surface scattering occurs.
Volumetric – Enables volumetric scattering. Useful for highly transparent materials that still scatter the refracted light. It is useful for liquids and other highly transparent materials. The Refraction Color has to be different than black for this effect to be visible. Please see the Translucency Mode Volumetric example below.
SSS – Enables non-transparent material scattering. Useful for skin, wax, marble, and other relatively opaque materials. Works independently of the Refraction Color and Refraction Glossiness. Please see the Translucency Mode SSS example below.

Translucency-None

Fog Color – Specifies the attenuation of light as it passes through the material. This option allows simulating the fact that thick objects look less transparent than thin objects. Note that the effect of the fog color depends on the absolute size of the objects and is therefore scene-dependent unless the Fog Units Scaling is enabled. The fog color also determines the look of the object when using fog scattering. For more information, please see the Fog Color Parameter examples below.

Fog Depth (cm) – Smaller values reduce the effect of the fog, making the material more transparent. Larger values increase the fog effect, making the material more opaque.

Translucency-Volumetric

Fog Color – Specifies the attenuation of light as it passes through the material. This option allows simulating the fact that thick objects look less transparent than thin objects. Note that the effect of the fog color depends on the absolute size of the objects and is therefore scene-dependent unless the Fog Units Scaling is enabled. The fog color also determines the look of the object when using fog scattering. For more information, please see the Fog Color Parameter examples below.

Depth (cm) – Controls the strength of the fog effect. Higher values reduce the effect of the fog, making the material more transparent. Smaller values increase the fog effect, making the material more opaque.

Scatter Color – An additional color filter in Volumetric scattering mode. In SSS translucency mode, this is the main sub-surface color and could potentially determine the overall material appearance.

SSS Amount – Controls the scattering effect contribution.

Translucency-SSS

Scatter Radius – Controls how deep rays travel within the medium for sub-surface scattering light evaluations.

Scale (cm) – Controls the strength of the sub-surface scattering effect. Grayscale values work best in this case.

SSS Color – An additional tint for the scattering effect. The main parameter controlling the scattering color is the Fog Color.

SSS Amount – Controls the scattering effect contribution.

Affect Shadows – When enabled, the material casts transparent shadows, depending on the refraction color and the fog color. This only works with V-Ray shadows and lights.

Fog Units Scaling – When enabled, the fog color attenuation becomes dependent on the current system unit.

Max depth – Specifies the number of times a ray can be refracted. Scenes with lots of refractive and reflective surfaces may require higher values to look right.

Affect channels – Specifies which channels are affected by the transparency of the material.

Color Only – The transparency of the material affects only the RGB channel of the final render.
Color+Alpha – Causes the material to transmit the alpha of the refracted objects instead of displaying an opaque alpha. Note that currently this works only with clear (non-glossy) refractions. 
All Channels – The transparency of the material affects all channels and render elements.

Trace Refractions – Enables/disables refraction tracing for the current material. The option disables only the refraction and not the transparent shadows. To make the shadows opaque, disable the Affect Shadows checkbox or set the Refraction Color to black.

Translucency set to None

Translucency set to Volumetric

Translucency set to SSS