Mirrors Formula

Mirrors are reflective surfaces that form images by reflection.

The Formula

1f=1do+1di\frac{1}{f} = \frac{1}{d_o} + \frac{1}{d_i}

When to use: A mirror sends light back in a predictable way, so your eye traces the rays and sees an image.

Quick Example

A plane mirror forms an upright virtual image, while a concave makeup mirror can magnify your face when held close.

Notation

ff is focal length, dod_o is object distance, did_i is image distance, and mm is magnification.

What This Formula Means

Mirrors are reflective surfaces that form images by reflection. Physics courses usually study plane mirrors and curved mirrors such as concave and convex mirrors.

A mirror sends light back in a predictable way, so your eye traces the rays and sees an image.

Formal View

For spherical mirrors, the mirror equation is 1/f=1/do+1/di1/f = 1/d_o + 1/d_i, and magnification is m=−di/do=hi/hom = -d_i/d_o = h_i/h_o.

Worked Examples

Example 1

medium
A concave mirror has f=15 cmf=15\text{ cm} and the object is at do=45 cmd_o = 45\text{ cm}. Find did_i and the magnification.

Answer

di=22.5 cm, m=−0.5d_i = 22.5\text{ cm},\ m = -0.5

First step

1
1/di=1/15−1/45=3/45−1/45=2/451/d_i = 1/15 - 1/45 = 3/45 - 1/45 = 2/45.

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Example 2

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A makeup mirror is concave with f=20 cmf = 20\text{ cm}. To get a 2×2\times upright image, where must the face be placed?

Example 3

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A concave mirror's image is half the size of the object and inverted, with the object at do=60 cmd_o = 60\text{ cm}. Find ff.

Common Mistakes

  • Mixing up real and virtual images. - Fix this by naming the system, checking "Am I tracking how light travels through space or materials, including boundary rules and image location when needed?", and attaching units or direction to the final statement.
  • Using object distance and image distance with the wrong sign convention. - Fix this by naming the system, checking "Am I tracking how light travels through space or materials, including boundary rules and image location when needed?", and attaching units or direction to the final statement.
  • Using mirrors from a keyword alone - Signal words like light, ray, image only point to a possible model; the system must match too.
  • Substituting numbers before defining the system - A formula cannot repair a missing object, boundary, direction, medium, or circuit path.

Why This Formula Matters

Mirrors helps students explain vision, lenses, mirrors, cameras, fiber optics, and astronomy. It turns what looks like a drawing rule into a physical model of how light carries information.

Frequently Asked Questions

What is the Mirrors formula?

Mirrors are reflective surfaces that form images by reflection. Physics courses usually study plane mirrors and curved mirrors such as concave and convex mirrors.

How do you use the Mirrors formula?

A mirror sends light back in a predictable way, so your eye traces the rays and sees an image.

What do the symbols mean in the Mirrors formula?

ff is focal length, dod_o is object distance, did_i is image distance, and mm is magnification.

Why is the Mirrors formula important in Physics?

Mirrors helps students explain vision, lenses, mirrors, cameras, fiber optics, and astronomy. It turns what looks like a drawing rule into a physical model of how light carries information.

What do students get wrong about Mirrors?

Students often know a formula related to mirrors but skip the recognition step: Am I tracking how light travels through space or materials, including boundary rules and image location when needed? That leads to a correct-looking substitution attached to the wrong physical model.

What should I learn before the Mirrors formula?

Before studying the Mirrors formula, you should understand: reflection.

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