Subjects optics

Lens Power Addition 6Afabd

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1. The problem asks to find the combined SPHERE power when adding two lenses given in minus cylinder format. 2. Each lens power is given as SPHERE - CYLINDER x AXIS. 3. Lens 1: $+0.69 - 3.00 \times 150$ and Lens 2: $-3.10 - 5.05 \times 060$. 4. To add lenses, convert each to their two principal powers (at axis and axis + 90 degrees): - For Lens 1: - $P_1 = S + C = 0.69 - 3.00 = -2.31$ - $P_2 = S = 0.69$ - For Lens 2: - $P_1 = S + C = -3.10 - 5.05 = -8.15$ - $P_2 = S = -3.10$ 5. Add the principal powers: - $P_1^{total} = -2.31 + (-8.15) = -10.46$ - $P_2^{total} = 0.69 + (-3.10) = -2.41$ 6. Convert back to minus cylinder form: - Sphere $S = P_2^{total} = -2.41$ - Cylinder $C = P_1^{total} - P_2^{total} = -10.46 - (-2.41) = -8.05$ - Axis is the axis of the cylinder from Lens 1, which is $150$ degrees. 7. Final combined lens power is $-2.41 - 8.05 \times 150$. 8. This is already in minus cylinder format and no rounding was done.