Question 5: Units , Dimensions and Error Analysis

Question

Two light rays A and B travel from a medium into air at angles of incidence 15 degrees and 42 degrees respectively. In the medium, light travels 3 cm in 0.2 ns . Will there be total internal reflection? If so, which ray?

Accepted Answer

First, find the refractive index of the medium:
Ã¢ÂÂ¢ Speed in medium
$$v=\frac{3\ 	ext{cm}}{0.2\ 	ext{ns}}=\frac{0.03\ 	ext{m}}{2	imes10^{-10}\ 	ext{s}}=1.5	imes10^8\ 	ext{m/s}$$
Ã¢ÂÂ¢ Refractive index
$$n=\frac{c}{v}=\frac{3	imes10^8}{1.5	imes10^8}=2$$
Next, the critical angle for total internal reflection at a mediumÃ¢ÂÂair interface (nÃ¢ÂÂÃ¢ÂÂ1) is
$$\sin	heta_c=\frac{n_{m air}}{n_{m med}}=\frac{1}{2}\quad\Longrightarrow\quad	heta_c=30^\circ$$
Compare with the incidence angles:
Ray A: 15ÃÂ°  30ÃÂ° Ã¢ÂÂ total internal reflection
Answer: Yes, only ray B (Option C).

Answer

No

Answer

Yes, A

Answer

Yes, B

Answer

Yes, Both A and B

Units , Dimensions and Error Analysis

Two light rays A and B travel from a medium into air at angles of incidence 15 degrees and 42 degrees respectively. In the medium, light travels 3 cm in 0.2 ns . Will there be total internal reflection? If so, which ray?

Choose the correct answer: