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Crystalline lens of the eye. The crystalline lens of the eye is double convex and has a typical index of refraction of $1.43 .$ At minimum power, the front surface has a radius of 10.0 $\mathrm{mm}$and the back surface has a radius of 6.0 $\mathrm{mm}$ ; at maximum power, these radii are 6.0 $\mathrm{mm}$ and 5.5 $\mathrm{mm}$ , respectively (although the values do vary from person to person). (a) Find the maximum and minimum power (in diopters) of the crystalline lens if it were in air. (b) What is the range of focal lengths the eye can achieve? (c) At minimum power, where does it focus the image of a very distant object? (d) At maximum power, where does it focus the image of an object at the near point of 25 $\mathrm{cm} ?$

a) 115 dioptersb) The focal length range is $[6.67 c) A distant object is focused at $[8.7 \mathrm{mm}]$ at minimum power.d) 6.85 $\mathrm{mm}$

Physics 102 Electricity and Magnetism

Physics 103

Chapter 25

Optical Instruments

Electromagnetic Waves

Reflection and Refraction of Light

Rutgers, The State University of New Jersey

University of Michigan - Ann Arbor

Hope College

McMaster University

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Okay, So for questions they was asking us with this the main minimum focal power and the maximum pull apart. Oh, this Look at the question for the focal par. So all arms equal to one over focal lens, which is you, Goto and minus one times one over. I want minus one grounds who and is the index of refraction I want is the radius off the front service and onto is the radius off the back service. So the maximum power is equal to and minus one times one over a one Macs minus one over R to mix and index numbers. Givens 1.43 and the maximum radius is given as, ah six millimeter, which is six times 10 to the power of negatory, you know, and our to Max Excuse Negative 5.5 million mirror, which is negative 5.5 times tens of power next to in years. The reason why here the art of Maxie's equal to minus 5.5 million here is because because here, the direction off the Prosser is this positive things are two years the back surface, the radius of back service that means of back is considered a negative direction. And that's why is equal to negative 5.5 million a year here. Okay, so if we plugging. So the equation we got P max is equal to n minus one with just 1.43 times one over our max, which is given its ah six well, over six times chance for about the next three meter minus one over minus, uh, my point by times. Change our power off. Negatory. Okay, Meter. And this will give us the maximum power is equal to while 50 people meters saying reporters, my bay say I DePorter, it's how this about a reporter, the openers doctors, the orbiter's Okay, Now let's do get Ah, Veneman. Focal power, which is equal to and minus one times one over. Ah one. Minutemen minus. While there are two many men, and this will give us pay minimum the power amendment. Legal to one point for me. Minus one. Let me double check things. Ah, see here of a lot of minus one year, so minus one times. Okay, open. Uh, okay. One point for three. Minus one times. One over. I believe the be in the middle radius off the brasseries was given as 10 millimeter, which is 10 times send to a power off 93 year. And that minus one over minus six point old may mean it was just six times Tinto Barrow 93 me there. And this will give us that minimum power. Beagles. Who? Long 115. The old quarters. Your burgers. Okay, if we take a look at that question, be so the question be was asking us with this arrange of folk Elin's, They're the I can, but she Okay, so well, we know that P is equal to one over f. So from this equation, we know that if have increase p increase. Okay, outfield deep Bruce. Which means that, um, uh is equal to one over p. Okay, so you have increase MPD Greece. So never He's f Max is equal to one over p minimum. Okay, which is equal to one over 1 15 deal voters, which is equal to about 6.67 men here. Okay. And the minimum vocal is will you go to one over? He maximum So the maximum power. Okay. And as equals one over 1 50 The openers and now give us is about a point seven millimeter. So the wrench off Focal A's. He's from 6.67 millimeter to 8.7. Man, you so full questions. See, it was asking us a minimum power. Where does he focused the image? Okay, it's a member. Well, this kind of question so and then empower the focal lens was given as, uh, after Minuteman. The missy was given as, uh, max was 8.7 millimeter. Okay, So the distant object of the images foreign at the focal focus. So which means that you will focus the image at a focal lens, which is the maximum folkways in this case. So 8.7 millimeter is the answer for this one. Okay. And for question D, it was asking us work has focused the image of an object at a near point off 25 7 years. Well, we know that one over half is equal to one or V plus one over you, in his case is the image distance you is the object distance. So in this case, you is given as 25 centimeters. Okay? And he's saying that the is at maximum power So have here, Mr Amendment, Just the minimum focal lens, which is six points at 67 millimeter. So we can, uh I'll be he's just simply equal to you. See these equal to I mean, that would shake have past you over you. Mine is, uh okay, u minus That. So you will be able to six point 67 men you manner, which is 6.67 times 10 to Apollo. Name. Three meter times 25 centimeter, which is 25 times 10 to the power off naked. Two year divided by you Want is F which is Tony via ties. A sense of how negative. Mir minus 6.67 times times about off next three meter. Okay. And this will give us The answer is about, um So the image distance servile zero point 00 six a five meter, which is 6.85 millimeter. So and maximum power it will, folks, the image of it object at a near point of 25 centimeter at six point if I millimeter okay. And that's my solution for the question. Thank you.

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