How the background becomes blurred when the aperture is large?

What is the science behind narrow depth of field at high aperture? When the aperture opening is small, what I am expecting is a circular cropped image as result. But it appears to be more complicated. Could someone please explain?

In a camera system, light coming from the outside world is converged by the lens and falls on the sensor/film. Object at the focus point is converged very sharply to the sensor. Object in the background will be converged to a point behind the sensor, which creates a blurred image at the sensor.

See the picture below.

The object A is in the focus and thus it creates a sharp image at the sensor. While object B is behind the focus plane and hence it creates a bigger and blurry image at the sensor.

When the aperture becomes smaller, the the scattered rays are eliminated from entering the lens and the image becomes sharper. When the aperture is small, the amount of light falling on the sensor will be less too. Hence we may have to keep the ISO high and/or shutter speed low.

The last image shows the working of a pin hole camera. There is no lens present at all. But in this case the light reaching the sensor will be too less. So the shutter speed shall be kept very low in order to get an image on the sensor.

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Thanks @reddot

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Well said Reddot

Never knew this!!

Great tutorial. Thanks