Lenses in contact
Powers add up, so opticians simply add.
Testing eyes
During an eye test, an optician puts several lenses, one touching the other, in the testing spectacles' frame. Each lens has a known power.
How might the optician find the power of the whole set of lenses?
What this lesson covers
The idea
The net power of lenses placed in contact is the algebraic sum of their individual powers: P = P1 + P2 + P3 + …
Testing eyes
During an eye test, an optician puts several lenses, one touching the other, in the testing spectacles' frame. Each lens has a known power.
How might the optician find the power of the whole set of lenses?
- By adding the powers of the lenses, with their signs
- By multiplying the powers
- By taking only the largest power
Two lenses touching
Use the two sliders to set the power of each lens. Read the net power. Do the book's example first.
Simple addition
The net power was the sum of the two. A convex lens adds a positive power and a concave lens a negative one. The book's example: +2.0 D and +0.25 D make +2.25 D. Because the powers simply add, opticians prefer powers to focal lengths.
The net power P of lenses placed in contact is the algebraic sum of their individual powers: P = P₁ + P₂ + P₃ + …. For example, lenses of +2.0 D and +0.25 D are equivalent to a single lens of +2.25 D.
Notes
Lenses in contact: P = P₁ + P₂ + P₃ + …, the algebraic sum of their powers.
Check yourself
Lenses are placed in contact. How is the net power found?
Two lenses in contact have powers +2.0 D and +0.25 D. What is the net power, in dioptres?
Answer: 2.25 D
P = P₁ + P₂ = (+2.0) + (+0.25) = +2.25 D.
A convex lens of +3.0 D is placed in contact with a concave lens of −1.0 D. What is the net power, in dioptres?
Answer: 2 D
P = (+3.0) + (−1.0) = +2.0 D.
Why is it convenient for an optician to use powers rather than focal lengths?
- By adding the individual powers with their signs — correct. Yes!
- By adding the focal lengths. It is the powers that add. Focal lengths do not simply add.
- By multiplying the powers. The book gives the net power as the algebraic sum, P = P₁ + P₂ + P₃ + …
- A lens of larger power has a longer focal length. Power is 1/f, so a lens of larger power has a shorter focal length.
- The net power of lenses in contact is found by simple addition — correct. Yes!
- Powers are measured in centimetres. Power is measured in dioptres. The focal length in metres gives the power.