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Current time:0:00Total duration:2:12

welcome back now that you're getting comfortable with the simple lens law let's go a little deeper in the previous exercise you found that the simple lens law can be written as I equals o times f / o minus f so if the image plane in our camera is at distance I objects at distance o from the camera will come into crisp focus but what about objects at some other distance well they'll be blurry they're not in crisp focus for example the in focus leaves are at a distance that satisfies the simple lens equation however the objects in the background are blurred out and notice how the blur is in the shape of a circle recall from the last lesson we call this a circle of confusion but how big is the circle to answer that question and the rest of this lesson will develop a formula that describes the size of the circle given things like the focal length of the lens the aperture and the distance to the object as before let's look at this problem in 2d and consider what happens to a point P with coordinates x0 y0 at a distance o from the lens we can intersect the parallel and medial rays to find the point where P comes into focus let's call this a and remember every lens has an aperture which restricts which rays make it into the camera let's put a point E at the center of our lens and a point D at the top of the aperture in other words D E is the radius of our aperture so all light rays from P which pass through de end up focusing at the same point a and if the image plane is at this distance eye then P will be in sharp focus but if the image plane is at a larger distance I prime say over here then P's image gets blurred out into the region denoted BC in the diagram this distance BC defines the size of the circle of confusion that is BC is the radius of the blur okay let's pause here so you can get comfortable with this diagram before we finish our calculation