# measuring refractive index of liquid using lens and mirror

by blackcat
Tags: index, lens, liquid, measuring, mirror, refractive
 P: 59 hi i've got to do measure hte refractive index of a liquid with mirror and lens first of all how can i measure hte refractive index of air in this way? i dont get how i can do this, please explain :| and then for the liquid, ive been told to put the liquid over the mirror and then the lens on top of the liquid, and then hold up a pin until it coincides with something, but i dont understand that. please hlep!
 HW Helper Sci Advisor P: 1,772 The refractive index of air is 1.0003 . Unless you have very good measuring devices, I don't immediately see how you are to measure that. Usually, it is assumed to be 1.000 unless you need extreme precision. Are you sure you have conveyed the requirements correctly? ARe you perhaps supposed to measure the focal length of the lens in air?
P: 59

## measuring refractive index of liquid using lens and mirror

Yeah,

Apparently i have to hold a pin above the lens and find out where the image coincides, I dont know what that means.
 HW Helper P: 1,446 Hold the pin held horizontally above the lens. The lens should be resting on the mirror. Move the pin vertically untill its image coincides with the real pin (you see both in focus simultaneously). This gives you the focal length of the convex lens, $f_1$, the distance from the pin to the lens. Repeat the process with the lens resting in the liquid on the mirror. The liquid lens is then a plano-convex lens with the same radius of curvature as the convex lens, $r$. This gives you their combined focal length, $F$. You can now calculate the focal length of the liquid lens from $$\frac{1}{F} = \frac{1}{f_1} + \frac{1}{f_2}$$ (it should be negative). Using the lens maker's equation for the liquid lens we next get that $$n_{liq} = 1 + \frac{r}{f_2}$$ for the refractive index of the liquid. In this formula r is also negative for the liquid lens. If you know the refractive index of the convex lens it can be shown that $$n_{liq} = 1 - 2(n_{lens} - 1)\frac{f_1}{f_2}$$
 P: 59 Thanks for your reply. But I have no idea what you mean by "its image coincides with the real pin (you see both in focus simultaneously)", I'm not even sure where to hold the pin with respect to the lens horizontally. I suppose I can ask my teacher. Thanks for your help with the equations.
 HW Helper P: 1,446 An convex lens will form a real image of the pin if the object distance is equal to or further than the focal length of the lens. Such image can be viewed with the eye if you position yourself looking up against the rays, that is in this case looking down onto the mirror. If the image do not coincide with the real pin your eye will only be able to focus on the one or the other (image or object). When the real pin and its image is simultaneously in focus we know that they are both in the same plane. This happens when the real pin (and the image) is at the focus of the lens. So what you need to do is move the pin vertically up and down until you see the image and the pin both in focus simultaneously. Allow me to correct myself. What you should be looking for is relative motion between the real pin and its image when you move your head slightly in a horizontal direction. If the two are not in the same plane you will observe that the pin and image seem to move separately when you move your head. When they are in the same plane you will observe that they move in unison. So while you move the pin up and down shake your head slightly (saying no) and observe the relative motion of the pin and its image.
 HW Helper P: 1,446 Slight correction to previous post.
 P: 59 Thanks For The Reply And Sorry For Not Posting This Before!
 HW Helper P: 1,446 I will try and post a photograph of such a setup soon. How did it go with the experiment?
 P: 59 It went well (I think). However I haven't worked out the refractive index yet cuz I need to figure out the radious of hte curvature of the lens (the equation needs it). Am I right in saying that the radius of the curvature of the lens (I read it in a book) is v in: 1/v = -1/u + 1/f Again thanks for you all your help.
 P: 59 I've realised that v can't = radius of curvature cause if you change u then v will change............. Is there any way to measure the radius of curvature of the lens without being in a lab? I have a mirror, lens and pin... Also, what would you say is a typical value for the radius of curvature of a convex lens with focal length 10cm and diameter 50mm? Thanks.
HW Helper
P: 3,033
 Quote by blackcat Is there any way to measure the radius of curvature of the lens without being in a lab? I have a mirror, lens and pin... Thanks.
There is a relationship between the focal length of the lens, its index of refraction, and the radii of curvature of its surfaces. I think it was already posted earlier.

http://hyperphysics.phy-astr.gsu.edu...pt/lenmak.html

Come to think of it, you could measure the radius of curvature of the lens if you can see reflections in the lens surface. Have you done the experiment to find the focal length of a convex mirror? The focal length of a spherical mirror is half the radius of curvature.

http://hyperphysics.phy-astr.gsu.edu/Hbase/hframe.html
 P: 59 Yeah, but I have to find using an alternative method that doesn't involve refractive index and/or lens maker's equation etc. And I havent done that experiment :( There has to be another way.
HW Helper
P: 3,033
 Quote by blackcat Yeah, but I have to find using an alternative method that doesn't involve refractive index and/or lens maker's equation etc. And I havent done that experiment :( There has to be another way.
There is another way, but it may be difficult to make the measurements. There is a device called a spherometer for measureing the curvature of a surface, but you probably do not have one of those laying around. You could accomplish what it does if you could make very accurate thickness measurements with a micrometer or vernier caliper, and if your lens is symmetrical (same radii on both sides). A very accurate measurement of the thickness of the lens in the middle, and at a known distance from the center (25mm) can be used to find the radius of curvature. Most thin lenses are not knife sharp on the edge, so you might want to move in a bit and make an actual measurement just inside the radius. Is this a possibility?
 P: 59 I'll take a look if my brother has one. I found an article in Wikipedia about it: http://en.wikipedia.org/wiki/Spherometer My lens is symettrical (it looks it), so I guess if I find one of those it should work properly?
 P: 59 Do you think -0.07 is a sensible figure for the radius of curvature?
HW Helper