High School

Four camera lenses have the following focal lengths and f-numbers:

A. 150 mm, f/1.2
B. 150 mm, f/5.6
C. 35 mm, f/1.2
D. 35 mm, f/5.6

Rank these lenses in order of increasing aperture diameter. Indicate ties where appropriate.

Answer :

Rank of Lenses (in increasing aperture diameter) is D. (35, f > 5.6), B (150, f > 5.6), C (35, f > 1.2), and A (150, f > 1.2).

The relationship between the aperture diameter (D), f-number (f), and focal length (F) of a lens is given by the formula:

[tex]D = \frac{F}{f}[/tex]

Using this formula, we can compute the aperture diameter for each lens:

  1. Lens A: Focal Length = 150 mm, f > 1.2
    For an f-number of 1.2: [tex]D = \frac{150}{1.2} = 125[/tex] mm
    (This is the maximum aperture diameter based on f > 1.2.)

  2. Lens B: Focal Length = 150 mm, f > 5.6
    For an f-number of 5.6: [tex]D = \frac{150}{5.6} \approx 26.79[/tex] mm
    (This is the maximum aperture diameter based on f > 5.6.)

  3. Lens C: Focal Length = 35 mm, f > 1.2
    For an f-number of 1.2: [tex]D = \frac{35}{1.2} \approx 29.17[/tex] mm
    (This is the maximum aperture diameter based on f > 1.2.)

  4. Lens D: Focal Length = 35 mm, f > 5.6
    For an f-number of 5.6: [tex]D = \frac{35}{5.6} \approx 6.25[/tex] mm
    (This is the maximum aperture diameter based on f > 5.6.)

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