Lens – Angle of View

Angle of View

The angle of view decreases when the focal length increases.

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The four photographs below are taken with a zoom lens with a variable focal length ranging from 70 mm to 200 mm. As the focal length increases, the angle of view becomes smaller and the depth of field reduces.

Angle of View Calculation

The diagonal angle of view α = 2 arctan d 2f is calculated from the focal length ( f ) and the diagonal ( d ) of the light sensitive surface.

Dimensions

The diagonal ( d ) is calculated from the dimensions of the light sensitive surface with the Pythagorean theorem a2 + b2 = c2 . Or, apllied here as d = b 2 + h 2 with width ( b ) and height ( h ) of the light sensitive surface.

Light Sensitive Surface Ratio

This image shows the ratio between common film and sensor sizes.

Smartphones and compact cameras achieve good resolution with small sensors. The middle of this camera part contains an image sensor of ~ 6.16 x 4.55 mm (1/2.3” ).

Angle of View Table

This table shows different angles of view for common focal lengths at a full-frame (24x36mm) size of the light sensitive surface.