Optics: Understanding Compound Lenses, Focal Lengths, and Diopters, Slides of Physics

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Compound Lens

Two Lenses

 A single convex lens produces

a real image.

 That image can be acted on by

a second lens.

• Second image can be real or virtual

Touching Lenses

1 2

1 2 f f

f f f 



 Two lenses are often brought

into close contact.

• Very short distance between optical centers

 The combined focal length can

be approximated.

• Let so 1 approach infinity
• Applies to convex and concave lenses 1 2

1 1 1 f f f

 

Farsighted

 Some eyes have weak

muscles.

• Near image focuses in front of the retina
• Hyperopia and presbyopia

 A compound converging lens

compensates for the eye’s

lens.

• Forces the image forward in the eye.

Diopters

 Optometrics works on corrective lenses for eyes.

 Diopters measure the inverse of the focal length of the

lens.

• 1 D = 1 m-
• Positive converging
• Negative diverging

 

  

     1 2

1 1 ( 1 )

1

R R

n f

D

so si

1 1 D 

Reading Glasses

 A person sees blurred print at

25 cm, but is fine at 125 cm.

 Find the diopter correction

needed.

next

 The diopter formula can be

applied to object and image

distances.

• Object is at 0.25 m
• Virtual image is at 1.25 m
• Correction needed is +3.2 D

1. 25 m

1

1. 25 m

1 1 1



    so s i

D