The Lens Clock (Geneva Lens Gauge): 1.530 Calibration Index, True Curvature Math & Index Correction Factors

The lens clock features two outer fixed pins separated by chord distance $2y$ (typically $20.0\ \text{mm}$, so $y = 10.0\ \text{mm}$) and a spring-loaded central mobile pin. Placing the instrument onto a lens surface depresses the center pin by sagitta depth $s$:

$$F_{\text{clock}} = \frac{2000 \cdot (n_{\text{cal}} - 1) \cdot s}{y^2} \quad \text{where } n_{\text{cal}} = 1.530 \text{ (Crown Glass Standard)}$$

Mechanical gears rotate the needle to indicate surface power directly in diopters based strictly on $n = 1.530$.

Because modern lenses are made of CR-39 ($1.498$), Polycarbonate ($1.586$), MR-8 ($1.600$), MR-7 ($1.660$), or MR-174 ($1.740$), the number displayed on the dial is NOT the true surface power ($F_{\text{true}}$). The true optical surface power is given by the Index Ratio:

$$F_{\text{true}} = F_{\text{clock}} \cdot \left( \frac{n_{\text{actual}} - 1}{n_{\text{cal}} - 1} \right) = F_{\text{clock}} \cdot \left( \frac{n_{\text{actual}} - 1}{0.530} \right)$$

Conversion factors across modern materials:

• CR-39 ($n=1.498$): $F_{\text{true}} = F_{\text{clock}} \times \frac{0.498}{0.530} = \mathbf{0.940 \cdot F_{\text{clock}}}$ (Clock over-reads by $6\%$).
• Polycarbonate ($n=1.586$): $F_{\text{true}} = F_{\text{clock}} \times \frac{0.586}{0.530} = \mathbf{1.106 \cdot F_{\text{clock}}}$ (Clock under-reads by $10.6\%$!).
• High-Index 1.74 ($n=1.740$): $F_{\text{true}} = F_{\text{clock}} \times \frac{0.740}{0.530} = \mathbf{1.396 \cdot F_{\text{clock}}}$ (Clock under-reads by an astonishing $\mathbf{39.6\%}$!).

Rotating the lens clock $360^\circ$ on a spherical surface leaves the needle completely stationary. If the needle oscillates between maximum and minimum values, the surface is toric (astigmatic) or mechanically warped by a pinched eyewire.