Question

in the following ray diagram calculate the speed of light in the liquid of unknown refractive index

Answer 1

Answer:

Explanation:

Refer the image

Answer 2

Answer:

The speed of light in the liquid of unknown refractive index is $1.8 \times 10^8 \mathrm{~m} / \mathrm{s}.$

Explanation:

Transparent material such as air, water, and glass slow down light. The refractive index of the medium is the ratio by which it is slowed, and it is always higher than one.

Step 1: Refractive index measures the bonding of light when travelling from one medium to another. The refractive index is the ratio of the speed of light in the vacuum to that in the air.

$n=\frac{c}{v}$

Step 2: As shown in Fig. 11(b) 11, ray $O A$ is suffering total internal reflection at A and going along

$A B$. $\therefore \angle O A N=C$, the critical angle.

$\begin{aligned}\mu & =\frac{1}{\sin C}=\frac{1}{C A / O A}=\frac{O A}{C A}=\frac{\sqrt{30^2+40^2}}{30} \\& =\frac{50}{30}=\frac{5}{3}\end{aligned}$

Step 3: As

$\mu=\frac{c}{v}$,

therefore,

$v=\frac{c}{\mu}$

$v=\frac{3 \times 10^8}{5 / 2}=\frac{9}{5} \times 10^8 \mathrm{~m} / \mathrm{s}=1.8 \times 10^8 \mathrm{~m} / \mathrm{s}$.

Hence, The speed of light in the liquid of unknown refractive index is $1.8 \times 10^8 \mathrm{~m} / \mathrm{s}.$

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