When a drop of water is placed on a flat, clear surface such as a glass slide or plastic sheet, surface tension pulls the top surface into a curved, lens-like shape so that the drop functions as a simple magnifier. Suppose a drop of water has a maximum angular magnification of 3.50. (a) Find the drop’s focal length. (b) Assuming the bottom surface of the drop is flat, use the lens-maker’s equation from Topic 23 to calculate the radius of curvature of the top surface.
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in this problem. The maximum angular magnification provided by the drop of water is 3.5. So too So the part, eh? To find the focal length of the drop. We know after maximum magnification. That and Max is one plus 25 centimeter over F, which is for the normal. I normal in Europe, we die. So from here, we can find focal length F to be 25 centimeter over M max minus one. And this is gonna be 25 centimeter over 2.5. And this will give me tense interview her, which is 0.1 meter. Okay, so to solve the part B, we're going to use the lengths makers equation. So I'm just gonna go to next page for this to solve part B. The lens equation lens makers equation is one over F because and minus one times one of her are one minus one of her are too. So the value of n, which is refractive index year for the drop of water is 1.33 and are one We're assuming one side is flat. So are one is going to be infinity radius of curvature of flat side and are, too, is what we're trying to find out. All right, so from here, we can actually do one over F because 1.33 minus one won over. Our one is one of the infinity. So that's going to be zero. So zero minus one over R two. All right, so from here, we can actually find out the magnitude of our two. That's what we care about actually is going to be. You can see it. This goes here. So that means that means 1.33 minus one is going to be 0.33 times magnitude of the focal length. Okay. And this is going to be 0.33 times 0.1, which is serial 0.33 meter war, 3.3 centimeter. So this is the radius of curvature of the curvy side.