Optics equations

Question 1

𝐿′ = 𝐿 + F

Answer 1

Vergence equation
𝐿′ = 𝐿 + F

𝐿′= image vergence
L= object vergence
F= dioptric power of the optical system

Question 2

𝐹′ = 𝑛′−𝑛/r

Answer 2

Single surface power equation
𝐹′ = 𝑛′−𝑛/r

n’=the index of ref of the final media
n= the index refraction of the original media
F= the power of the SSRI (single spherical refractive Interfaces)

Question 3

𝑀 = 𝑦′/𝑦 = 𝑛∙𝑙′/𝑛′∙𝑙 = 𝐿/𝐿′

Answer 3

Lateral magnification aka linear magnification

𝑀 = 𝑦′/𝑦 = 𝑛∙𝑙′/𝑛′∙𝑙 = 𝐿/𝐿′

y'= height of image
y= height of object
l'= image distance from the lens
l= object distance from the lens
L'= image vergence/ outgoing vergence
L= object vergence/ incoming vergence

• in thin lenses only*
• 𝑀 = 𝑙′/𝑙

Question 4

𝑃 = 𝑑 ∙ F

Answer 4

Prentice rule

𝑃 = 𝑑 ∙ F
* remember d is in cm!

• P= prismatic effect
• decentration (𝑑) in cm, lens power (𝐹) in diopters
• Prentice’s rule is a simplification based on small angle approximation

Question 5

𝑛′/𝑙′ = 𝑛/l

Answer 5

Apparent depth

𝑛′/𝑙′ = 𝑛/l

Question 6

F = F1 + F2

Answer 6

In thin lenses, calculate the power of each and then add them together to get the total lens power

F= F1 + F2

Question 7

𝑛=𝑐/𝑣

Answer 7

Refractive index

𝑛=𝑐/𝑣

Question 8

𝐹=(𝑛′−𝑛)∙(1/𝑟1 −1/𝑟2 )

Answer 8

Lens maker’s equation

𝐹=(𝑛′−𝑛)∙(1/𝑟1 −1/𝑟2 )

𝑛′= refractive index of the lens material
𝑛= refractive index of the surrounding medium 
𝑟1= front surface radius
𝑟2= back surface radius

in air
𝐹=(𝑛−1)∙(1/𝑟1 −1/𝑟2 )

Question 9

𝐹𝑥=𝐹/(1−𝑑𝐹)

Answer 9

Effective power

𝐹𝑥=𝐹/(1−𝑑𝐹)

𝐹𝑥= the desired power at the cornea
F= the power of the correcting lens needed at a vertex distance of d

• If 𝑥 (i.e. the new lens) is located to the right of the original lens position, 𝑑 has a positive value
• If 𝑥 (i.e. the new lens) is located to the left of the original lens position, 𝑑 has a negative value