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Old Jan 25th 2016, 04:40 AM   #1
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Refractive index of glass block

A student wants to find the refractive index of a rectangular block of glass. He draws around the block and marks the position of a ray of light that travels through the block. With the block removed, the student can draw in a normal line and then measure the angle of incidence and the angle of refraction. The student repeats this process for different angles of incidence. His measurements are shown in the table.

Angle of incidence Angle of refraction

10 ............................... 6.5
20 .................................. 13
30 ...................................20
40 ................................. 25
50 ....................................32
60 ..................................35


Snells law
Refractive index = (sin i / sin r)


What was the independent variable in this investigation? What was the dependent variable?

Independent variable is the angle of incidence (because it is the one that can be varied).

Dependent variable is the angle of refraction (because it is dependent on the angle of incidence).


Have I got the independent and dependent variables mixed up?

I'm concerned because I read somewhere that :
x-axis = independent variable
y-axis = dependent variable.

But later in the question in the book it says: Draw a graph of sin i (y-axis) against sin r (x-axis).
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Old Jan 25th 2016, 07:08 AM   #2
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Originally Posted by Hero View Post
AWhat was the independent variable in this investigation? What was the dependent variable?

Independent variable is the angle of incidence (because it is the one that can be varied).

Dependent variable is the angle of refraction (because it is dependent on the angle of incidence).


Have I got the independent and dependent variables mixed up?
No, you are not mixed up - your answer is correct.

Originally Posted by Hero View Post
I'm concerned because I read somewhere that :
x-axis = independent variable
y-axis = dependent variable.
Yes, that is usually how graphs are drawn (but not always).

Originally Posted by Hero View Post
But later in the question in the book it says: Draw a graph of sin i (y-axis) against sin r (x-axis).
I think it asks you to do this because Snell's Law is equal to sin i/sin r, and so drawing the graph this way will result in a best-fit straight line whose slope is equal to the index of refraction.
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Old Jan 26th 2016, 01:09 PM   #3
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Independent variable is the angle of incidence ...... so this is usually the x-axis

Dependent variable is the angle of refraction ..... so this is usually the y-axis

But in this question I've been asked to draw angle of incidence as the y-axis
and angle of refraction as x-axis.

Is just an ODD case where the rule does not apply?

If I didn't know what the independent variable and dependent variable for this question ..... then I could be clever and notice (further along in the question) that I've been asked to "draw a graph of sin i (y-axis) against sin r (x-axis)" ..... then I could simply (incorrectly) assume that angle of incidence must be the dependent variable because this is the y-axis and make the same mistake for the independent variable.
I WOULD GET THE ANSWER WRONG
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Old Jan 26th 2016, 01:37 PM   #4
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Yes, it's odd, and yes, it's good that you are smart enough to know they have asked you to make a plot that swaps the usual convention of independent and dependent axes. You asked "why" they are making you do this, and I gave a reasonable explanation - does it make sense to you?
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Old Jan 26th 2016, 02:50 PM   #5
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Yes thanks I understood your explaination.


I thought the rule that x-axis = independent variable and y-axis = dependent variable was fixed in stone.

So now I know its a general rule and if I'm stuck on what is the independent variable and dependent variable in a particular experiment is ..... I can look at the graph and take a punt that the x-axis is the independent. Now i know it will only be a punt and its better to know the proper answer
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Old Jan 27th 2016, 06:43 AM   #6
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A picture is worth 1000 words

A graph is just a tool to help you visualise the relationship between to parameters.
Differently scaled axes are often used when the relationship between the parameters is not a simple linear relationship (the graph is not a simple straight line).
In the olden days (when I were a lad) we had packs of special graph paper where one (or sometimes both) axis would be logarithmic (for example).

I suggest you try plotting the data both ways (if you have Excel then plotting two graphs will be barely more time consuming than plotting one).
The benefits of the different axes should then become evident.

Note that one set of axes may be better for showing one feature of the data
while a different set of axes might highlight another feature of the data.
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