# Which of these concave lenses has a greater power

Let's say that a concave lens $$A$$ has a focal length of $$-10$$ $$cm$$ and another concave lens $$B$$ has a focal length of $$-20$$ $$cm$$ and we need to compare their powers.

We know that : $$P(D) = \dfrac{1}{f(m)}$$ Here, $$P(D)$$ means the power of the lens in dioptres (D) and $$f(m)$$ means the focal length of the lens in metres (m).

Here, $$f_A=-10$$ $$cm$$ and $$f_B = -20$$ $$cm$$.
So, $$P_A = -10D$$ and $$P_B = -5D$$.

Now, mathematically thinking, $$-5 > -10$$, so $$P_B > P_A$$ and hence $$B$$ should have a greater power.
But, logically thinking, lens $$B$$ has a focal length of $$-10$$ $$cm$$ and lens $$B$$ has a focal length of $$-20$$ $$cm$$. So, rays parallel to the principal axis will seem to meet $$10$$ $$cm$$ from the optical centre upon refraction from lens $$A$$ and $$20$$ $$cm$$ from lens $$B$$. So, the rays are diverging more in the case of lens $$A$$ since they appear to meet closer to the optical centre.

So, in my opinion, lens $$A$$ is more powerful than lens $$A$$ and we should compare the powers of concave lens by looking at the absolute values of their focal lengths and powers when comparing and negative values for magnitude and nature of the lens.
For example, $$|P_A| = 10D \text { and }|P_B|=5D$$ $$\text {So, }|P_A| > |P_B|$$ Thus, lens $$A$$ is more powerful than lens $$B$$

Let me know if I'm right.
Thanks!

• Please fix the question: there are a couple of places where a lens is pronounced to have a different focal length or be more powerful than the same lens. Feb 27, 2022 at 14:10

Your first step, that mathematically speaking $$-5\:\mathrm D>-10\:\mathrm D$$, is correct but in lenses that negative sign only represents which type of lens it is. So lens $$A$$ has greater power than $$B$$.