Lenses and Mirrors

The Lens Formula

Lenses form images by refracting light, and mirrors form images by reflecting it.

• Lens formula: 1/F = 1/d + 1/f.
• Optical power: D = 1/F, its unit is the diopter.
• Magnification: Γ = f/d.

Here d is the distance from the object to the lens, f is the distance from the image to the lens, and F is the focal length. If the focal length is taken in meters, D comes out in diopters. For a virtual image, f is taken as negative; for a diverging lens, F is taken as negative.

Images

Optical device	Image
Converging lens, d = 2F	f = 2F, real, inverted, same size
Converging lens (in general)	real or virtual
Diverging lens	always virtual, upright, reduced
Plane mirror	virtual, same size, as far behind the mirror as the object is in front

• For a spherical mirror, F = R/2.
• A diverging lens does not produce a real image.

Examples

• If F = 0,25 m, then D = 1/0,25 = 4 diopters.
• d = 25 cm, F = 20 cm: 1/f = 1/20 − 1/25 = 1/100, f = 100 cm. Γ = 100/25 = 4.