Question #287848

You can determine the index of


refraction of a substance by


determining its critical angle. (a) What


is the index of refraction of a


substance that has a critical angle of


68.4º when submerged in water?


What is the substance, based on Table


25.1? (b) What would the critical


angle be for this substance in air?



1
Expert's answer
2022-01-17T09:59:40-0500

Explanations & Calculations


  • For the first case,

ns.sinC=nw.sin90nsnw=1sinC=1sin68.4=1.076(w.r.t water)nsaair×nairnw=1.076nsnair=nsubstance=1.076×nwnair=1.076×1.33=1.43w.r.t air\qquad\qquad \begin{aligned} \small n_s.\sin C&=\small n_w.\sin 90\\ \small \frac{n_s}{n_w}&=\small \frac{1}{\sin C}\\ &=\small \frac{1}{\sin 68.4}=1.076\cdots(\text{w.r.t water})\\ \\ \small \frac{n_s}{a_{air}}\times\frac{n_{air}}{n_w}&=\small 1.076\\ \small \frac{n_s}{n_{air}}=n_{substance}&=\small 1.076\times\frac{n_w}{n_{air}}\\ &=\small 1.076\times1.33\\ &=\small 1.43\cdots{\text{w.r.t air}} \end{aligned}

  • You can find what the substance is referring the table for this value.


  • When the substance is in air,

ns.sinC=nair.sin90sinC=nair.1ns=11.43C=sin1(1/1.43)=44.40\qquad\qquad \begin{aligned} \small n_s.\sin C&=\small n_{air}.\sin90\\ \small \sin C&=\small \frac{n_{air}.1}{n_s}\\ &=\small \frac{1}{1.43}\\ \small C&=\small \sin^{-1}(1/1.43)\\ &=\small 44.4^0 \end{aligned}


Need a fast expert's response?

Submit order

and get a quick answer at the best price

for any assignment or question with DETAILED EXPLANATIONS!

Comments

No comments. Be the first!
LATEST TUTORIALS
APPROVED BY CLIENTS