The Glass Slab and the Travelling Microscope

Transcript

0:00Introduction

Hello everyone, here is a small puzzle before we start. Put a thick glass slab on a mark on your table, and look straight down. The mark seems to float up, inside the glass. Now suppose all you have is a microscope that slides up and down a scale. Can you find the refractive index of that glass with it? Yes, you can, with just three readings. This is part of experimental skills in JEE, and questions on these readings do come up. So, let's begin.

0:32The travelling microscope

So, look at the figure. Each box marked with a capital M is the same microscope, in three positions, and the orange dashed line is its line of sight, straight down. This is a travelling microscope, and its focusing distance is fixed. Okay? So let me ask you this. If the focusing distance is fixed, how do we bring an object into focus? Yes, exactly, we move the whole microscope up or down until the object is sharp. We do not alter its eyepiece or its tube. Right? Why does that matter? Because only then does the plane in focus stay at a fixed distance from the objective. So when the microscope shifts, the plane it focuses on shifts by exactly the same amount. With me? And the position of the microscope is read on a vertical scale fitted with a vernier. So each reading tells us how high the microscope stands. Clear?

1:30Three readings

Now the experiment itself, three readings, from left to right in the figure. First, with no slab, we focus on the black cross, a mark on the table. That reading is R one, capital R with a small one below it. Okay? Second, we place the slab over the mark and focus on the same mark, seen through the glass. That reading is R two. See the orange cross in the middle picture? That is where the mark now appears, raised inside the slab. Right? Third, we must focus on the top surface of the slab. In the third picture, the word powder marks a fine powder sprinkled on that top surface. Why do we need that powder? Because clean glass is transparent, its top surface offers nothing to focus on, and the powder marks it. We use a fine powder, lycopodium or chalk powder, the two names in brackets on screen. That reading is R three. Got it?

2:26Real and apparent thickness

Now, from the first reading to the third, the microscope moved from the mark on the table up to the top of the slab. So the real thickness is R three minus R one. Okay? Now tell me, what is the apparent thickness, the thickness the glass seems to have? Correct, it runs from the raised mark up to the top, so it is R three minus R two. Right? And the refractive index, the Greek letter mu, is the real thickness over the apparent thickness. So mu equals R three minus R one, over R three minus R two. This is the line to remember. Clear? Now, a small question for you. Is R two bigger or smaller than R one? It is bigger, because the mark appears raised, like the orange cross we saw in the figure, so the microscope goes up to refocus. The mark is raised by R two minus R one, and this equals the thickness, t, times, in brackets, one minus one over mu. Keep this shift separate from the apparent thickness, because students often mix them up. With me?

3:30Reading the scale

Now, a word about the scale. Usually the main scale is divided into half millimetres, so one main scale division is zero point five millimetres. Okay? And fifty vernier divisions are equal to forty nine main scale divisions. So what is the least count? The least count is zero point five millimetres over fifty, which gives zero point zero one millimetres. In centimetres, that is zero point zero zero one centimetres. That is why our readings in centimetres carry three decimal places. Right? And there is one more point. The same three readings give the refractive index of a liquid in a beaker too. We will do exactly that in Example two. Clear?

4:15Example 1: slab readings 2.150, 2.650, 3.650 cm, find mu

Now Example one, a direct one to start. The microscope readings are these. R one is two point one five zero centimetres, R two is two point six five zero centimetres, and R three is three point six five zero centimetres. Find the refractive index of the slab. Pause the video and try it first. Are you done? Okay, let us check it together. The real thickness is R three minus R one. Three point six five zero minus two point one five zero gives one point five zero zero centimetres. Okay? The apparent thickness is R three minus R two. Three point six five zero minus two point six five zero gives one point zero zero zero centimetres. Right? So mu equals one point five zero zero over one point zero zero zero, which gives one point five zero. Clear? Now here is a quick way to check it. The mark was raised by R two minus R one, which is zero point five zero zero centimetres. And the thickness, one point five zero zero, times one minus one over one point five, also gives zero point five zero zero. The two agree, so our readings are consistent. Very good if you got it.

5:28Example 2: refractive index of a liquid in a beaker

Now Example two, a little harder, with a liquid this time. For a liquid in a beaker, the readings are one point two zero zero centimetres for the mark at the bottom, with the beaker empty, then two point one zero zero centimetres for the mark seen through the liquid, and four point eight zero zero centimetres for the surface of the liquid. Find the refractive index. Pause the video and try it first. Are you done? Okay, let us check it together. Some students say the mark rose by two point one zero zero minus one point two zero zero, which is zero point nine zero zero. So mu is three point six zero zero over zero point nine zero zero, which gives four, right? That is the trap, so be careful, because zero point nine zero zero is how much the mark was raised, not the apparent depth. Let us do it properly. The real depth is the surface minus the mark, so four point eight zero zero minus one point two zero zero gives three point six zero zero centimetres. Okay? The apparent depth runs from the raised mark up to the surface. Four point eight zero zero minus two point one zero zero gives two point seven zero zero centimetres. Right? So mu equals three point six zero zero over two point seven zero zero, which is four over three. The wavy equals sign means approximately, so mu is about one point three three. Very good if you divided by the apparent depth, and not by the shift.

7:01Quick revision: three readings, mu = real over apparent

So, quick revision. Focus by moving the whole microscope, and read its position on a vertical scale with a vernier. Take three readings: the mark, the mark through the slab, and the powder on top. Then mu equals R three minus R one, over R three minus R two, and the mark is raised by R two minus R one, which equals the thickness, t, times, in brackets, one minus one over mu. Now go and try the practice problems on this page, and all the very best to you.