A lens forms an of an object. The object is 16.0 cm from the lens. The is 12.0 cm from the lens on the same side as the object. (a) What is the focal length of the lens? Is the lens converging or diverging?

Video transcript

Hi everyone. In this practice problem, we will be asked to determine the focal length and find whether the lens is convergent or divergent. We will have a photocopier machine using a thin lens to make an image of a document on its drum. The image is then used to make the copy where a password is put on the photocopier machine's document glass which is 20 centimeter away from the lens and the image form is 15 centimeters from the lens and is on the opposite side. We're being asked to determine the focal length and find out whether the lens is converging or diverging. And the option C of an R A F equals 8.6 centimeter and converging B F equals negative 7.4 centimeter and converging C F equals negative 60 centimeter and diverging and D F equals centimeter and diverging. So the 10 months equation is going to be expressed as one divided by F equals to one divided by D O plus one divided by D I F is going to be the focal length of the lens D O which will be equals to 20 centimeter is the distance of the object from the lens and D I which will be 15 centimeter is the distance of the image formed from the lens. The image distance is positive since the image is located on the opposite side. So therefore the image is going to be real and positive. You wanna remember that the focal length or F for converging lens is going to be zero. So uh bigger than zero. So F bigger than zero for converging and for a diverging lens, F will be uh negative or smaller than zero just like. So as we have the relationship listed here already, what we need to do is just plug in all the values. So we have one divided by F equals to one divided by D O which is one divided by 20 centimeter plus one divided by D I which is one divided by centimeter. Calculating this, we will get uh one divided by F to then be equals to taking the common denominator. We will have 60 centimeter for both. So uh the numerator will then be equals to three plus four. So then calculating for F F will equals to 60 centimeter divided by seven which will then come up to a value of 8. 70 m. So the focal length of the lens is 8.6 and since F is bigger than zero, then lens is going to be converging. So there we have the answer to this practice problem F will be equals to 8. centimeter and lens will be converging and those two will correspond to option A in our answer choices. So option A will be the answer to this particular practice problem. And that'll be it for this video. If you guys still have any sort of confusion, please feel free to check out our adolescent videos on similar topics available on our website. But other than that, that will be it for this video. Thank you so much for watching.