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

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

• A. Ms = 1/ (1- (t/n)D1)
• B. Ms = 1 - (t/n)D1
• C. Ms = 1/ (1+ (t/n)D1)
• D. Ms = 1 / (1 - tD1/n)

Answer: (A)

Shape factor shows how the physical thickness of a lens and its index alter the magnification you get with spectacles. In a thick lens, the principal planes don’t coincide with the lens surfaces, so the simple thin-lens magnification needs a correction that depends on how far light travels inside the lens and how strong the front surface powers. The amount of this correction is proportional to (t/n) times the front-surface power D1, where t is thickness and n is the lens index. To translate that internal shift into a change in magnification at the spectacle plane, you take the reciprocal of one minus that quantity, giving Ms = 1 / [1 − (t/n) D1]. This form neatly captures how increasing thickness or front-surface power (for a positive D1) pushes the shape factor away from 1, reflecting the thicker lens’s greater departure from the thin-lens prediction. The product (t/n) D1 can also be written as tD1/n, so the same relationship can be expressed in that arrangement as well. The sign and magnitude of D1 determine whether the correction increases or decreases magnification in a given situation.

Shape factor shows how the physical thickness of a lens and its index alter the magnification you get with spectacles. In a thick lens, the principal planes don’t coincide with the lens surfaces, so the simple thin-lens magnification needs a correction that depends on how far light travels inside the lens and how strong the front surface powers. The amount of this correction is proportional to (t/n) times the front-surface power D1, where t is thickness and n is the lens index. To translate that internal shift into a change in magnification at the spectacle plane, you take the reciprocal of one minus that quantity, giving Ms = 1 / [1 − (t/n) D1]. This form neatly captures how increasing thickness or front-surface power (for a positive D1) pushes the shape factor away from 1, reflecting the thicker lens’s greater departure from the thin-lens prediction. The product (t/n) D1 can also be written as tD1/n, so the same relationship can be expressed in that arrangement as well. The sign and magnitude of D1 determine whether the correction increases or decreases magnification in a given situation.