The Daleks produced by the Progenitor had radically redesigned eyepieces with black rings on the stick, fins on the cone, and the lens being organic rather than robotic. The viewpoint from this eyepiece is similar except for an opaque orange perimeter with honeycomb circuitry and protruding organic veins. (TV: Victory of the Daleks)
With a wide-angle lens, the eyepiece could magnify images so that the Dalek could see across great distances and also track a person's footsteps. (TV: Destiny of the Daleks) The eyepiece was the most vulnerable part of the Dalek. Dalek eyestalks from a post-Last Great Time War era were capable of even greater forms of magnification, with various scales displayed in-vision.
The viewpoint from the eyepiece varied over time, from a simple telescope-like view (TV: The Dalek Invasion of Earth) to an infrared scanner (TV: Destiny of the Daleks) to a bright green (or white, in the case of Imperial Daleks) lens, with Kaled script readouts displayed in the top and bottom left corners. (TV: Remembrance of the Daleks) By the time of the Last Great Time War, the eyestalks all contained blue glowing lenses, with a targeting aid "on-screen" at all times. (TV: Dalek)
When the eyepiece was destroyed or covered, the Dalek became a reduced threat. After the eyepiece was destroyed, its head would spin around uncontrollably and the Dalek's weapon would be fired in a blind panic, usually accompanied by the frantic screaming of "My vision is impaired— I cannot see!". (TV: Revelation of the Daleks)
Whilst on Skaro in order to escape from the Dalek base, the Fourth Doctor threw his hat onto a Dalek's eyestalk, the Dalek began firing incandescently guided by Davros, and almost hitting Davros in the process until the Doctor destroyed it. (TV: Destiny of the Daleks)
During the Shoreditch Incident, Ace fired an ATR (Anti-tank rocket) at an Imperial Dalek and was shocked at the damage. She responded by saying "I aimed for the eyepiece.". While inside a Dalek shuttle craft, the Seventh Doctor merely placed his hat on a Dalek's eyepiece to confuse it while he "shorted it out". (TV: Remembrance of the Daleks)
However, post-Time War Daleks overcame this exploitable weakness. Their shielding could resist most bullets (however bastic bullets were still effective). They could also melt any hinderance, as Wilfred Mott discovered when he shot a Dalek eyestalk with a paintball gun. The paint was immediately melted off and the Dalek was heard to say "My vision is not impaired.". (TV: The Parting of the Ways, The Stolen Earth)