What is the formula for the Power factor of a thick lens when calculating spectacle mag?

What is the formula for the Power factor of a thick lens when calculating spectacle mag?

• A. MP = 1/(1-hDv)
• B. MP = 1/(1+hDv)
• C. MP = 1/(1 - hDv^2)
• D. MP = 1 - hDv

Answer: (A)

The essence is how the distance from the eye to the back surface of the spectacle (the vertex distance) interacts with the lens power at that back surface to change the size of the image seen through the glasses. The back-vertex power, Dv, combines with the vertex distance, h, to give a simple, first-order factor that modifies magnification. This factor is the reciprocal of 1 minus the product h × Dv, so the power factor equals MP = 1 / (1 − hDv). Here h is in meters and Dv in diopters, making the product dimensionless. This form captures the idea that the eye-lens separation and the lens power together influence how large the image appears; plus powers (positive Dv) and the actual vertex distance increase the factor in a way that aligns with common experience of spectacle magnification, while minus powers and larger separations reduce it. The other options don’t fit because they either omit the reciprocal, involve a squared power term, or place a plus sign where the established relationship uses a minus in the denominator.

The essence is how the distance from the eye to the back surface of the spectacle (the vertex distance) interacts with the lens power at that back surface to change the size of the image seen through the glasses. The back-vertex power, Dv, combines with the vertex distance, h, to give a simple, first-order factor that modifies magnification. This factor is the reciprocal of 1 minus the product h × Dv, so the power factor equals MP = 1 / (1 − hDv). Here h is in meters and Dv in diopters, making the product dimensionless.

This form captures the idea that the eye-lens separation and the lens power together influence how large the image appears; plus powers (positive Dv) and the actual vertex distance increase the factor in a way that aligns with common experience of spectacle magnification, while minus powers and larger separations reduce it. The other options don’t fit because they either omit the reciprocal, involve a squared power term, or place a plus sign where the established relationship uses a minus in the denominator.