Question

8. Submit, along with this report file, a scatter plot of sin 02 as a function of sino 1 0.9 0.8 0.7 0.6 Sin theta 2 0.5 0.4 0.3 0.2 0.1 0 0 0.2 y = 0.2442x + 0.2471 0.4 0.8 1 1.2 0.6 Sin theta 1 9. Record the equation for the best fit line: y = 0.2442x + 0.2471 10. What is the measured ratio of the indices of refraction ni/n2? |

the question also says to use snell's law to find the ratio. but i am kind of confused as to how to do this using the graph and line of best fit. please help..!

Answer 1

As I can see you have mistakenly put the 2nd data point as (0.173, 0.87) instead of the real data point (0.173, 0.087). That's why you got the wrong $\sin \theta_{1}\; vs\; \sin \theta _{2}$ graph, hence resulting the wrong equation of best fit line.

Here I have calculated the slope of best fit line properly. Though it doesn't pass exactly through origin(as it should because when incident angle is zero the refracted angle must also be zero) , we can assume it happened due to experimental errors.

I have measured the mean of the x-variables($\sin \theta_{1}$) to be 0.6212 and y-variables(
sin e
) to be 0.3205. From here I have calculated $\sum_{i=1}^{10}(x_{i}-\bar{X}) (y_{i}-\bar{Y})=0.628571$ . And $\sum_{i=1}^{10}(x_{i}-\bar{X})^{2}=1.1368516$ . So from these two values I got the slope of the graph to be 0. 553.​​​ Hence the value is $\frac{\eta _{1} }{\eta _{2}}=0.553$ , as from Snell's law we get $\frac{\eta _{1} }{\eta _{2}}=\frac{\sin _{2}}{\sin _{1}}$ .

So from the best fit line we can conclude $\frac{\sin \theta_{2} }{\sin \theta _{1}}=0.553$ which is close to the theoretical value 0.75.