Problem

CE Jurassic Park A $T$ rex chases the heroes of S…

03:18

Problem 86 Easy Difficulty

The focal length of a lens is inversely proportional to the quantity $(n-1),$ where $n$ is the index of refraction of the lens
material. The value of $n,$ however, depends on the wavelength of
the light that passes through the lens. For example, one type of
flint 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 placed
24.00 $\mathrm{cm}$ in front of a lens made from this type of glass. If the red
light reflected from this object produces a sharp image 55.00 $\mathrm{cm}$
from the lens, where will the violet image be found?

Answer

see work

Related Courses

Physics 103

Discussion

You must be signed in to discuss.

Top Physics 103 Educators

Christina K.

Rutgers, The State University of New Jersey

Watch More Solved Questions in Chapter 26

Problem 1

Problem 2

Problem 3

Problem 4

Problem 5

Problem 6

Problem 7

Problem 8

Problem 9

Problem 10

Problem 11

Problem 12

Problem 13

Problem 14

Problem 15

Problem 16

Problem 17

Problem 18

Problem 19

Problem 20

Problem 21

Problem 22

Problem 23

Problem 24

Problem 25

Problem 26

Problem 27

Problem 28

Problem 29

Problem 30

Problem 31

Problem 32

Problem 33

Problem 34

Problem 35

Problem 36

Problem 37

Problem 38

Problem 39

Problem 40

Problem 41

Problem 42

Problem 43

Problem 44

Problem 45

Problem 46

Problem 47

Problem 48

Problem 49

Problem 50

Problem 51

Problem 52

Problem 53

Problem 54

Problem 55

Problem 56

Problem 57

Problem 58

Problem 59

Problem 60

Problem 61

Problem 62

Problem 63

Problem 64

Problem 65

Problem 66

Problem 67

Problem 68

Problem 69

Problem 70

Problem 71

Problem 72

Problem 73

Problem 74

Problem 75

Problem 76

Problem 77

Problem 78

Problem 79

Problem 80

Problem 81

Problem 82

Problem 83

Problem 84

Problem 85

Problem 86

Problem 87

Problem 88

Problem 89

Problem 90

Problem 91

Problem 92

Problem 93

Problem 94

Problem 95

Problem 96

Problem 97

Problem 98

Problem 99

Problem 100

Problem 101

Problem 102

Problem 103

Problem 104

Problem 105

Problem 106

Problem 107

Problem 108

Problem 109

Problem 110

Problem 111

Problem 112

Problem 113

Problem 114

Video Transcript

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.

Get More Help with this Textbook