optics - Would obstacles cause light diffraction if it has the same refractive index as the surrounding material?

Restatement of title:

Would an obstacle still cause diffraction of light if it has the same refractive index as the surrounding material?

Answer

Generally speaking we use the term diffraction when we have some apparatus that blocks part of the light. So for example a diffraction grating absorbs light except at the slits in it. When no light is being absorbed we normally use the term refraction. They're both the same physics, but the distinction is often convenient. Your question implies the obstacle doesn't absorb light, so your question is about refraction not diffraction.

Anyhow, refraction relies on different regions of the light encountering media with different refractive indices. The differing refractive index causes a path dependant phase change in the light that leads to refraction. In the case you describe where the refractive index is everywhere constant there will be no refraction.

This is used in the measurement of refractive indices of powders. If you do first year crystallography at university you are likely to do a practical where you measure the refractive index of a powdered mineral by placing the powder in liquids of different refractive indices and measuring the light absorption. When the refractive index of the powder is the same as the refractive index of the liquid the powder becomes virtually invisible and the light absorption falls to almost zero.