Computer Vision Foundations · free preview

The Lensmaker's Formula

The sphere as the focusing surface, the formula relating object distance, image distance, radius and index, and why off-axis points focus too.

1. A sphere satisfies the condition

A sphere satisfies the condition

2. The lensmaker's formula

The lensmaker's formula

3. Pairs of conjugate points

Pairs of conjugate points

4. What the focal length means

What the focal length means

5. Two lenses, one stronger

Two lenses are cut from glass with the same refractive index, and the first has a radius of curvature of 1010 centimeters while the second has a radius of 55 centimeters. Both are single surfaces. Which lens has the shorter focal length?

6. An object at infinity

A camera lens of focal length f=50f = 50 millimeters is aimed at a star, an object effectively at infinite distance. Where does the image of the star form?

7. Focal length from a conjugate pair

A lens forms a sharp image when the object sits a=50a = 50 centimeters in front of the glass and the sensor sits b=50b = 50 centimeters behind it. Using 1/a+1/b=1/f1/a + 1/b = 1/f, compute the focal length in centimeters and write the number.

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