How to determine Refractive Index without using the Refractive Angle?

[jonas_28]

Homework Statement

A Lateral Displacement Experiment of a laser beam pass through a rectangle glass block in environment, AIR (n1=1.00). By measuring the Incident Angle and Lateral Displacement on the Screen WITHOUT measuring Refractive Angle. Form an equation to relate the lateral displacement (d) and incident angle (θ1).

Relevant Equations

Snell's Law

 

[Steve4Physics]

Homework Statement:: A Lateral Displacement Experiment of a laser beam pass through a rectangle glass block in environment, AIR (n1=1.00). By measuring the Incident Angle and Lateral Displacement on the Screen WITHOUT measuring Refractive Angle. Form an equation to relate the lateral displacement (d) and incident angle (θ1).
Relevant Equations:: Snell's Law

View attachment 284794
View attachment 284793

Hi @jonas_28. Welcome to Physics Forums.

Your diagram shows angles $\theta_i$ and $\theta_0$. I guess these are what you call $\theta_1$ and $\theta_2$. Also the diagram doesn't show distance $l$ but I guess this is what is shown as AB on the diagram. It is worth checking for consistency before posting.

Are you familiar with inverse trig' functions? If $sin(y) = x$ then $y = sin^{-1}x$.

In your working x is $\frac {n_1}{n_2} \sin\theta_1$ and y is $\theta_2$.

 

[kuruman]

You know that $\sin\theta_2=\dfrac{n_1}{n_2}\sin\theta_1$ and you want to eliminate $\cos\theta_2$ from your expression for $d$. Well, you also know that $\cos^2\theta_2+\sin^2\theta_2=1.$ So $\dots$

 

[rsk]

A version of this experiment appears fairly often in one of the IGCSE 'alternative to practical' papers - but as a practical exercise without the theory, ie the students measure it and perform the calculations without having to follow the theory. (eg Q5 here)

For those who don't know, IGCSE is the International version of the UK's General Cert of Secondary Education, with exams sat at age 15-16.