When an optician prescribes a-5D lens, what does it mean?

The power of a lens (P) is defined as the reciprocal of its focal length (f) in meters, expressed as P = 1/f [c3][t3]. According to standard sign conventions, the focal length and power of a convex (converging) lens are positive, while those of a concave (diverging) lens are negative [c4][t1][t6]. In this case, the prescribed power is -5D. The negative sign immediately identifies the lens as concave [c4][t3]. To find the focal length, we use the formula f = 1/P. Substituting the given value, f = 1/(-5) meters, which equals -0.2 meters [t2][t10]. Converting this to centimeters (0.2 * 100), we get a focal length of 20 cm [t3][t7]. Therefore, a -5D prescription signifies a concave lens with a focal length of 20 cm.

Sources

1. [1] Science , class X (NCERT 2025 ed.) > Chapter 9: Light – Reflection and Refraction > 9.3.8 Power of a Lens > p. 157
2. [2] Science , class X (NCERT 2025 ed.) > Chapter 9: Light – Reflection and Refraction > 9.3.6 Sign Convention for Spherical Lenses > p. 155