Sign convention for lenses

The idea

Lenses follow the same sign rules as spherical mirrors, but all distances are measured from the optical centre; the focal length of a convex lens is positive and that of a concave lens negative.

Same rules, new origin

You already know how signs work for a mirror: right and up are positive, left and down are negative. Lenses use a similar rule.

From which point do you think all distances are measured for a lens?

• The optical centre of the lens
• The principal focus
• The object

Signs for lenses

Look at where the origin is and at the sign of the focal length. Open every tab.

Measure from O

Everything is measured from O. Because the focus of a convex lens is on the right of O, its f is positive. The focus of a concave lens is on the left, so its f is negative.

For lenses we follow a sign convention similar to that for mirrors, but all measurements are taken from the optical centre. The focal length of a convex lens is positive and that of a concave lens is negative. Take care to use the right signs for u, v, f and the heights h and h′.

Notes

For a lens all distances are measured from the optical centre, with the mirror's signs. f is positive for a convex lens and negative for a concave lens.

Check yourself

From where are distances measured for a lens?

What is the sign of the focal length of a convex lens?

What is the sign of the focal length of a concave lens?

An object is placed 40 cm to the left of a lens. What is its object distance? Give the signed number in cm.

Answer: -40 cm

The object is to the left of O, so u = −40 cm.

• The pole. A pole belongs to a mirror. For a lens the distances are measured from the optical centre.
• The principal focus. The focal length is itself a distance measured from the optical centre to the focus.
• The optical centre — correct. Yes!
• Positive — correct. Yes!
• Negative. The focal length of a concave lens is negative.
• It has no sign. The focal length has a sign: positive for a convex lens, negative for a concave lens.
• Positive. The focal length of a convex lens is positive.
• Negative — correct. Yes!
• Zero. A concave lens has a definite focal length. It is negative.