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When shooting portraits it is generally a good idea to blur the background in order to emphasize the person and avoid distraction from the background.

Blurring the background is done by shooting with a lower f/number (i.e., wider aperture). The portrait mode on a point 'n shoot camera selects a low f/number (wide aperture) for you.

The optimal f/number varies a bit based on the distance you are from the person, lens focal length, and how much background blur you want.

The portraits of Ama and Naomi in this collection were shot at f/2.8. That is, a low f/number (wide aperture), thus creating a shallow depth-of-field in order to focus on the face alone.

The portrait of Beau with his mother was shot at f/6.3 (i.e., somewhat higher f/number, meaning narrow aperture/ more depth-of-field) to blur the mother, but not so much that you are unable to see her expression.
BeauAmaNaomiBaby Beau Blues