Dielectric polarization and compressibility — interpreting static vs optical dielectric constants Assertion (A): If the difference between the static dielectric constant and the optical dielectric constant of a material is high, the material's mechanical compressibility is also high. Reason (R): For soft ions, the ionic polarization produced per unit electric field is higher than for hard ions.

Introduction / Context:
The static dielectric constant of an insulating solid includes all polarization mechanisms (electronic, ionic, and possibly orientational), whereas the optical dielectric constant reflects only the very rapid electronic polarization that can respond at optical frequencies. The gap between these two values indicates the strength of “slower” ionic polarization, which is closely related to how easily ions can be displaced in the crystal (mechanical softness/compressibility).

Given Data / Assumptions:

• Static dielectric constant includes electronic and ionic contributions.
• Optical dielectric constant approximates the purely electronic contribution.
• “Soft” ions are more easily displaced; “hard” ions are comparatively rigid.
• Linear, small-field polarization regime is assumed.

Concept / Approach:
If the difference (static − optical) is large, the ionic term is large. A large ionic polarizability implies weaker restoring forces in the lattice and hence higher mechanical compliance (higher compressibility). Soft ions, by definition, exhibit larger displacement per unit electric field, which increases the ionic polarization component.

Step-by-Step Solution:
Identify that static ε contains electronic + ionic; optical ε ≈ electronic only.A large difference means substantial ionic polarization.High ionic polarizability ↔ lower force constants ↔ higher compressibility.Soft ions provide larger ionic polarization per field than hard ions, directly explaining A.

Verification / Alternative check:
Lyddane–Sachs–Teller type relations link dielectric response to optic phonon frequencies; lower phonon frequencies (softer lattice) correlate with higher static ε relative to the high-frequency ε.

Why Other Options Are Wrong:
Stating that R is false or not explanatory contradicts the physical linkage between ionic softness, ionic polarization, and compressibility.

Common Pitfalls:
Confusing orientational polarization (important for polar molecules) with ionic polarization in crystals; assuming optical ε includes ionic response (it does not).

Final Answer:
Both A and R are true and R is correct explanation of A