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The focal length of a lens is inversely proportional to the quantity $(n-1),$ where $n$ is the index of refraction of the lensmaterial. The value of $n,$ however, depends on the wavelength ofthe light that passes through the lens. For example, one type offlint glass has an index of refraction of $n_{\mathrm{r}}=1.572$ for red light and $n_{v}=1.605$ in violet light. Now, suppose a white object is placed24.00 $\mathrm{cm}$ in front of a lens made from this type of glass. If the redlight reflected from this object produces a sharp image 55.00 $\mathrm{cm}$from the lens, where will the violet image be found?

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Physics 103

Chapter 26

Geometrical Optics

Wave Optics

Cornell University

Rutgers, The State University of New Jersey

University of Michigan - Ann Arbor

McMaster University

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this question, given that the focal length lenses investing proportional to and minus one and it's a refractive index. And we also know that refractive index depends on the color of the light. So given a white object, yeah, I gives up white light, so they are really light. And while the light in it so and then the objects pays 24 c m from the lens and the image distance for the red light is 55 cm. Um, so the red light reflected from this subject produces a shop image 55 cm from the lens We want to find what's the image distance when while the light is shining on the white object. Okay, so to do this will be using the the thing lands formula. Mhm. He's the tenants formula say is one of you has one of the I guess it was, too. Did you go to one? Oh, F K. So, um, and seems focal line is proportional to, um one over and minus one one over f will be proportionate two and minus y mhm. And, um so I'm just going to write, uh, one over f is equal to a constant times and minus one. Okay, so just to make things easier, okay. For red light on our s uh, 1.572 So, uh, wonder where is equal to K times on 0.57 to minus one is equal to, uh, 0.572 Okay. Okay, then you are also given that Theo is 24 c m three I is 55 CN. Hey, double positive. Okay, so the equation becomes one of 24 plus 1/55. This is equal to ah, 0.572 k. Hey, Um yeah. And you can also, uh, combined er traction meaning the weapon site to get 79 by 1320 Okay, so, yeah. Then for the violet light on N V is equal to 1.605 So one of the F eyes equal to que times 1.605 minus one. This is equal to 0.605 k. Mhm. So you have 1/24. That's one over. E I Violet is equal to 0.605 k. Yeah. So we have two equations. Okay, so one do you want to? We have 79 derived by 13 to 0. Divide by 1. 24 plus one over E I common be Okay, This is equal to 0.52 Divide by 0.605 Yeah. Yeah. Maybe I put because we arranged this equation to make it. Yeah. Okay, then rearrange. Yeah, so we just do the algebra. Okay. And then So the image distance for violet light it is equally true. 0.605 Time 79 Divide by 13 to 0, minus your 0.572 Uh, if I buy 24 to the U. S. And they multiplied by 0.572 Okay, and then this is equal to 46.2 PM So this is the answer. What? This question and that's all.

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