BIO Ordinary Glasses. Ordinary glasses are worn in front of the eye and usually 2.0 cm in front of the eyeball. Suppose that the person in Exercise 34.52 prefers ordinary glasses to contact lenses. What focal length lenses are needed to correct his vision, and what is their power in diopters?

Video transcript

Hi, everyone in this practice problem, we're being asked to determine the focal length and also the power in diopters off an eye glasses. Well, you have a blurry, close up vision and an eye specialist measures your near point to be centimeter. The eye specialist tells you that you should wear eyeglasses. And if the distance between your eyeball and the glasses is 1. centimeter, we're being asked to determine the focal length of the required eyeglasses to adjust your vision and also express that answer in diopters. The options given are a negative 45.6 centimeter and negative 0.219 diopters B negative 15. centimeter and negative 6.3 diopters C 15. centimeter and 0.63 diopters. And lastly D 45.6 centimeter and 2. diopters. So we want the lens to form a virtual image of the object at the near point of the I 50 centimeter. So the object distance is going to equals two or s will equals to 25 centimeter minus 1. centimeter, which will then be equals to twe 23.5 centimeter. The virtual image is on the incoming side of the eyeglass lens or then prime will be equals to negative 50 centimeter plus 1.5 centimeter which will then be equals to negative 48.5 centimeter. We wanna recall or utilize the object image relationship for a lens where one divided by S plus one divided by S prime will be equals to one divided by F. And in this case, through some rearrangement, we want to uh get an equation for F or the focal length, which is what's being asked in this practice problem. So then through summ rearrangement F will then equals to S multiplied by S prime divided by S plus S prime. So we can actually substitute the S and the S prime that we just determined into our focal length uh formula here. So S is 23.5 centimeter and then S prime is negative 48.5 centimeter defied that by S which is 23.5 centimeter plus four plus negative 48.5 centimeter through some calculation that will give us a value for the focal length F to then be equals to 45.6 centimeter. So the focal length of the eyeglasses is going to be 45.6 centimeter. Next, we want to express this answer or the power in diopters. So power in diopter is going to equal to one divided by F. So in this case, power will then equals to one divided by 45.6 centimeter or we have to convert that two m so that we have one divided by 0.456 m meter. So that will give us a 2.19 diopters of the power. So there we have it, the focal length of the required eyeglasses to adjust our vision is going to be 45.6 centimeter. And that answer in diopters or the power in diopters is going to be 2.19 diopters that will actually correspond to option D in our answer choices. So option D will be the answer to this particular practice problem. So that'll be it for this video. If you guys still have any sort of confusion, please make sure to check out our other lesson videos on our website and that'll be it for this one. Thank you.