# Essence of astronomy binoculars shopping

Shopping for astronomy binoculars can be complicated, and lots of terms are thrown around, such as magnification, diameter, weight, size, etc.

Is a 8x42 better than a 10x50? or a 20x60? What does that even mean?

## 1. Biology and Physics

In the dark, your eye’s pupil will dilate up to 5 to 7 mm after about 20 minutes.

As a consequence, any binoculars / telescope image should match this size, and no more. This is called the Exit Pupil Diameter (EPD).

On the other hand, the magnification of a binocular is defined as the ratio of the size of the input diameter over the diameter of the exit pupil:

\(M = \frac{D}{EPD}\)

## 2. Diameter to magnification table

Given that EPD is fixed, we can define the best magnification factor for a given diameter.

This answers the following question: If I want to get 30 mm binoculars, what magnification factor should they have?

Diameter (mm) | M (EPD = 5 mm) | M (EPD = 7 mm) |
---|---|---|

10 |
2 |
1.4 |

20 |
4 |
2.8 |

30 |
6 |
4.3 |

40 |
8 |
5.7 |

50 |
10 |
6.2 |

60 |
12 |
8.6 |

70 |
14 |
10 |

80 |
16 |
11.4 |

90 |
18 |
12.9 |

100 |
20 |
14.3 |

110 |
22 |
15.7 |

120 |
24 |
17.1 |

130 |
26 |
18.6 |

140 |
28 |
20 |

150 |
30 |
21.4 |

160 |
32 |
22.9 |

170 |
34 |
24.3 |

180 |
36 |
25.7 |

190 |
38 |
27.1 |

200 |
40 |
28.6 |

## 3. Magnification to diameter table

Similarly, we can ask the reverse question: If I want to get binoculars with a 12x magnification factor, what diameter should they have?

For a given magnification factor, what is the best diameter?

Note: this tables also reads like what is sold online: 10x50, 8x40, etc.

M | Diameter (EPD = 5 mm) | Diameter (EPD = 7 mm) |
---|---|---|

2 |
10 |
14 |

5 |
25 |
35 |

8 |
40 |
56 |

10 |
50 |
70 |

12 |
60 |
84 |

15 |
75 |
105 |

20 |
100 |
140 |

25 |
125 |
175 |

30 |
150 |
210 |

35 |
175 |
245 |

40 |
200 |
280 |

50 |
250 |
350 |

60 |
300 |
420 |

## 4. Conclusion

Given those two tables, next time you want to buy a pair of binoculars, you can quickly check what to look for, and what not to.