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# Thin Lenses; Ray Tracing

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<figure><img src="/files/fWDOdDaJ8IqiZ0GhPIN3" alt=""><figcaption></figcaption></figure>

<figure><img src="/files/qvYjAZBlnHPWXfFfTITK" alt=""><figcaption><p>Definition of Focal Point</p></figcaption></figure>

More precisely:

Focal Point: The image point of an object that is infinitesimally away on the lense that is on the lens axis.

<figure><img src="/files/rPtOxwwO5EFBSvVxcdWt" alt=""><figcaption><p>Evidence of Focal Point</p></figcaption></figure>

<figure><img src="/files/1B8Nbhxy44POQXHS78yZ" alt=""><figcaption></figcaption></figure>

<figure><img src="/files/IQhjxueanYMBlORQyA5w" alt=""><figcaption></figcaption></figure>

<figure><img src="/files/DOFULzOQ0Fevw5KDeP22" alt=""><figcaption><p>The third ray wouldn't normally do that unless it was infinitely thin.</p></figcaption></figure>

<figure><img src="/files/ZfkNYReDK3CW4bfH8022" alt=""><figcaption></figcaption></figure>

<figure><img src="/files/pkXdI7ATzc9BqaKCg3tM" alt=""><figcaption></figcaption></figure>

**Thin Lense Equation**

<figure><img src="/files/e8rSNSNmve06uPDjaOGf" alt=""><figcaption></figcaption></figure>

$$
\frac{1}{f}=\frac{1}{d\_i}+\frac{1}{d\_o}
$$

<figure><img src="/files/FpZtB3QGumup9SFLXLtx" alt=""><figcaption></figcaption></figure>

<figure><img src="/files/IG6tgGKcMSridrKepMD0" alt=""><figcaption></figcaption></figure>

<figure><img src="/files/phRxEk4SdMmnE72EHua5" alt=""><figcaption></figcaption></figure>

<figure><img src="/files/2x7LXXKG0aijO3ae36i0" alt=""><figcaption></figcaption></figure>

<figure><img src="/files/NbHrXUyCrUpH3pa8YNcX" alt=""><figcaption></figcaption></figure>

Answer: As closer objects require the lense to be further from the sensor, the image will approach the focal length as the distance increases and vice versa as the image gets closer.  ( think how the lenses move when a camera is focusing ).

<figure><img src="/files/UkecxfwuNLpwbKR2GqKK" alt=""><figcaption></figcaption></figure>

**Combination of Lenses**

<figure><img src="/files/VNN1ZLRCm3xGKYtsr7Wj" alt=""><figcaption><p>Object distance from second lens not equal to image distance from first lense</p></figcaption></figure>

<figure><img src="/files/2UEQbIIEbGdcGWFet2Za" alt=""><figcaption></figcaption></figure>

<figure><img src="/files/0bstHV5IfhWQ7j5CkTQs" alt=""><figcaption></figcaption></figure>
