# What is the sign convention for convex lens and concave lens? ## Biconvex lens

Lenses are found in a huge variety of optical instruments, from a simple magnifying glass to a camera zoom lens to the eye itself. In this section, we use Snell’s law to explore the properties of lenses and how they form images.

The word “lens” derives from Latin for a lens grain, whose shape is similar to that of a convex lens. However, not all lenses have the same shape. Figure 2.17 shows different lens shapes. The vocabulary used to describe lenses is the same as that used for spherical mirrors: The axis of symmetry of a lens is called the optical axis, the point where this axis intersects the lens surface is called the lens vertex, and so on.

Light rays entering (a) a converging lens and (b) a diverging lens, parallel to their axis, converge at their focal point F. The distance from the center of the lens to the focal point is the focal length f of the lens. Note that light rays are deflected in and out of the lens, with the overall effect of deflecting the rays toward the optical axis.

### It is the most common and useful representation of a diverging lens.

The focal length or focal length of a lens is the distance between the optical center of the lens and the focus (or focal point). The inverse of the focal length of a lens is the power, and is measured in diopters.

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For a thin lens that is in the air, the focal length is the distance from the center of the lens to any of the main foci (or focal points) of the lens. For a converging lens (e.g., a convex lens), the focal length is positive, and is the distance at which a collimated beam of light will be focused to a single point. For a diverging lens (e.g., a concave lens), the focal length is negative, and is the distance to the point over which a collimated beam appears to diverge after passing through the lens.

The focal length of a thin lens can be easily measured by using the lens to form an image of a distant light source on a screen. The lens is moved until a sharp image is formed on the screen. In this case 1/u is negligible, and the focal length is then given by:

### Diverging lens

In geometrical optics there are different standards and conventions that you can use to analyze problems. We recommend that you follow the DIN standard (initials of Deutsches Institut for Normung or German Institute for Standardization) also called European standard. However, at the end of this section we will present you, as a reference, another sign criterion that is also widely used.

Rays form positive angles to the principal axis or to any other axis when taking the ray to the axis by the shortest path in a counterclockwise direction. Rays form negative angles with the main axis or with any other axis when taking the ray to the axis by the shortest path we turn in the same direction as clockwise.

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If you find it difficult to remember the above criterion, remember that, in paraxial approximation, α≃tanα=opposite cathetuscontiguous cathetus , so you can deduce the sign from the sign of the distances corresponding to the opposite cathetus and contiguous cathetus.

### Convergent and divergent lens

Sign convention in opticsMaddy Why is the sign convention used in the derivation of lens formula and used again when applied in numerical problems? Won’t the whole idea of sign convention be eliminated if it is used twice?

Radha Krishna Actually, in the derivation of lens maker formula we apply the sign convention (Cartesian sign convention) twice, so it cancels out in the derivation. Then, in the problem, when we reapply the sign convention, we get the correct answer according to the sign convention. But personally for me, the classical sign convention is much easier to follow and solve problems. I use the following sign convention for lenses: i) The distances of the real object, the real image and the real focus (focal length) are positive, if they are not negative. ii) If the prime focus is in the densest medium, the focal length is positive. iii) If the incident ray bends towards the prime axis after refraction, then the image is real and if it bends, then the image is virtual.

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