2
$\begingroup$

My book defines the power of lens using this way:

The power P of a lens is defined as the tangent of the angle by which it converges or diverges a beam of light falling at unit distant from the optical centre $tan(x)=h/f$ and for small $x$ , $x=h/f$ , $h=1, x=1/f$. Thus power p of a lens is $p=1/f$.

The SI unit for power of a lens is dioptre (D): $1D = 1m^{–1}$. The power of a lens of focal length of 1 metre is one dioptre. Power of a lens is positive for a converging lens and negative for a diverging lens. Thus, when an optician prescribes a corrective lens of power $+ 2.5 D$, the required lens is a convex lens of focal length $+ 40 cm$. A lens of power of $– 4.0 D$ means a concave lens of focal length $– 25 cm$.

If power P of a lens is defined as a tangent of angle of convergence or divergence , the tangent is a dimensionless quantity! So its unit should not be $m^{-1}$ or $D$. Taking h=1 does not mean we negate its dimension right ?

$\endgroup$
2
  • $\begingroup$ Please consider using text instead of pictures, pictures get broken or lost in the internet very easily. $\endgroup$
    – Mauricio
    Commented Nov 23, 2023 at 18:45
  • $\begingroup$ Okay , just give me a few minutes @Mauricio $\endgroup$
    – Razz
    Commented Nov 23, 2023 at 18:47

1 Answer 1

1
$\begingroup$

Power is not the tangent of an angle. That would indeed be dimensionless.

$P = 1/f$, where $f$ is in meters. Thus the dimension of $p$ is $m^{-1}$.

$\endgroup$
2
  • $\begingroup$ Then the definition given in the book shouldn't be taken seriously, have they given it for intuitive purposes ? $\endgroup$
    – Razz
    Commented Nov 24, 2023 at 7:28
  • $\begingroup$ The book is being a little loose, saying $h=1$ and then ignoring $h$. Actually $P = tan(\theta)/h$. $\endgroup$
    – mmesser314
    Commented Nov 24, 2023 at 16:41

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.