Interpret the statement about polarization

A good polaroid completely removes the component of electric field along one direction and transmits only one plane of vibration. So the incident light on the prism is plane polarized.

Condition at Brewster's angle

When light is incident at the Brewster angle $i_B$ on a dielectric surface, the reflected and refracted rays satisfy $i_B + r = 90^\circ$ Hence, the reflected and refracted rays are perpendicular.

Also, for light polarized with electric field in the plane of incidence (i.e. $p$-polarized light), the reflection coefficient becomes zero at Brewster angle.

Use the clue from the polaroid statement

The phrase indicates that the electric field vector responsible for reflection is removed by the polaroid, so the incident light on the prism is polarized such that at Brewster angle there is no reflected ray.

Therefore, at Brewster angle for this suitably polarized light:

• reflection vanishes,
• the light is completely transmitted into the prism.

Check options

• A: Reflected and refracted rays are perpendicular at Brewster angle — this is true in general, but here the more relevant phenomenon for the polarized light is disappearance of reflection.
• B: Wave propagates along the surface — false.
• C: No refraction and total reflection — false.
• D: No reflection and total transmission — correct for plane-polarized light incident at Brewster angle.

Final conclusion

The most suitable option is $\boxed{\text{D}}$