Step 1: The phrase second sight describes an elderly patient who finds that reading suddenly becomes easier, occasionally being able to read newsprint without spectacles, which is a transient gift soon overtaken by worsening lens opacity.
Step 2: The optical reason is a rise in the refractive index of a hardening, sclerosing lens nucleus. A higher index lens bends light more strongly, inducing a myopic shift that brings near targets into sharp focus, an effect called index myopia.
Step 3: Since only nuclear sclerosis changes the index of the central lens substance, this phenomenon is tied exclusively to nuclear cataract.
Step 4: The remaining options act elsewhere in the lens, cortex, zonular lamellae, or punctate dots, and never increase nuclear refractive power, so they cannot give second sight.
\[\boxed{\text{Nuclear cataract}}\]