A lensmaker wants to make a magnifying glass from glass that has an index of refraction n = 1.55 and a focal length of 20.0 cm. If the two surfaces of the lens are to have equal radii, what should that radius be?

Video transcript

Hi, everyone in this practice problem, we're being asked to determine the radius when both surfaces of a lens will have the same radii. So Emily suffers from far sightedness and Emily went to an optical consultant to help her choose the perfect frame with the highest quality lens for her glasses. The glass that she opted for has an index of refraction of N equals to 1.45 a focal length of 15 centimeter. We're being asked to determine the radius when both surfaces of the lens have the same radii. And the options given are a 66.7 centimeter B 54.6 centimeter C 30 centimeter D 42.1 centimeter. So you'll recall the lens maker equation for a thin lens which we will use in this problem statement. So the lens maker equation for thin thin lens will be one divided by F equals two in parentheses and minus one close parenthesis multiplied by one divided by er O R one minus one divided by R two just like. So F here is the focal length of the lens N is the index of refraction of the lens material R one is the radius of curvature for the first surface R two is the radius of curvature for the second surface. And the two radii of the curvature will also follow the sign rules where R one and R two will be positive when the radius is in the back and negative when the radius is in the front and the focal is going to be positive when the lens is convergent and negative when the lens is di divergent. So in this case, we will get R one to be equal to R and R two will be equal to negative R. So then our equation will then be equals to one divided by F equals two and minus one multiplied by open parentheses. One divided by R, one will be one divided by R minus one divided by negative R negative R which is going to be plus R. So in this case, we will have one divided by F equals to N minus one multiplied by two divided by R. So next we want to plug in the values which is in this case is the focal length and also the N or the index of refraction for the lens. So one divided by F will be one divided by 15 centimeter which will be equals to N minus one, N will be 1.45. So 1.45 minus one multiply it by two divided by R and then calculating this we can then obtain the value for R. So R will then be equals to two multiplied by 15 centimeter divided by 0.45. Calculating this the R will come out to a value of 66. cent the meter. So there we have the uh radi R or the radius when both surfaces of the lens will have the same radii which is going to be R which is going to be equals to 66.7 centime meter. So there we have it 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 one. Thank you.