Lenses are precisely shaped pieces of glass that have been developed and used in corrective glasses, telescopes, microscopes, binoculars, and magnifying glasses.
If a lens has a shorter focal lengthThe distance between the centre of the lens and the focal point. it is said to be more powerful. The power of a lens is defined as the reciprocalThe reciprocal of a number is 1 divided by that number. The reciprocal of a fraction is that fraction turned upside down, eg the reciprocal of 3/4 is 4/3. of the focal length. Lens power is measured in dioptres (D).
\(power \ of \ a \ lens \ (D) = \frac{1}{focal \ length \ (m)}\)
\(P = \frac{1}{f}\)
Converging (convexAn object or shape that curves or bulges outwards, like a circle or sphere.) lenses have positive focal lengths, so they also have positive power values.
Diverging (concaveCurving inwards, rather than bulging outwards.) lenses have negative focal lengths, so they also have negative power values.
Example 1
What is the power of a convex lens with a focal length of 25 cm?
First convert focal length into metres: f = 25 cm = 0.25 m
\(lens \ power = \frac{1}{0.25} = 4.0 \ D\)
\(lens \ power = 4.0 \ dioptres\)
Example 2
A lens has a power of -3.33 dioptres. Calculate the focal length and state what type of lens it is.
\(f = \frac{1}{D}\)
\(f = \frac{1}{-3.33} = -0.30 \ m\)
\(focal \ length = -30 \ cm \ (concave \ lens)\)
Question
A convex lens has a focal length of 5.0 cm. Calculate the power of the lens.