Calculate the speed of light in a medium whose refractive index is 2.4

Answer:

Approximately [tex]1.3\times 10^{8}\; \rm m\cdot s^{-1}[/tex].

Explanation:

Look up the speed of light in vacuum: [tex]c \approx 3.00\times 10^{8}\; \rm m\cdot s^{-1}[/tex]. Denote the speed as [tex]c[/tex].

If the speed of light in a medium is [tex]v[/tex], the refractive index of that medium would be:

[tex]\displaystyle n = \frac{c}{v}[/tex].

Note, that the refractive index of a medium is inversely proportional to the speed of light in this medium. A medium with a larger refractive index would thus correspond to a slower speed of light.

Rearrange this equation to find the speed of light [tex]v[/tex] in this medium:

[tex]\begin{aligned}v &= \frac{c}{n} \\ &= \frac{3.00\times 10^{8}\; \rm m\cdot s^{-1}}{2.4} \\ &\approx 1.25 \times 10^{8}\; \rm m\cdot s^{-1}\end{aligned}[/tex].

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Read the excerpt below and then answer the question that follows:
The Book of Dragons
Chapter III The Deliverers of Their Country, an excerpt
By E. Nesbit

It all began with Effie's getting something in her eye. It hurt very much indeed, and it felt something like a red-hot spark—only it seemed to have legs as well, and wings like a fly. Effie rubbed and cried—not real crying, but the kind your eye does all by itself without your being miserable inside your mind—and then she went to her father to have the thing in her eye taken out. Effie's father was a doctor, so of course he knew how to take things out of eyes.

When he had gotten the thing out, he said: "This is very curious." Effie had often got things in her eye before, and her father had always seemed to think it was natural—rather tiresome and naughty perhaps, but still natural. He had never before thought it curious.

Effie stood holding her handkerchief to her eye, and said: "I don't believe it's out." People always say this when they have had something in their eyes.

"Oh, yes—it's out," said the doctor. "Here it is, on the brush. This is very interesting."

Effie had never heard her father say that about anything that she had any share in. She said: "What?"

The doctor carried the brush very carefully across the room, and held the point of it under his microscope—then he twisted the brass screws of the microscope, and looked through the top with one eye.

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"You might give me sixpence, Daddy," said Effie, "because I did bring you the new specimen. I took great care of it inside my eye, and my eye does hurt."

The doctor was so pleased with the new specimen that he gave Effie a shilling, and presently the professor stepped round. He stayed to lunch, and he and the doctor quarreled very happily all the afternoon about the name and the family of the thing that had come out of Effie's eye.

But at teatime another thing happened. Effie's brother Harry fished something out of his tea, which he thought at first was an earwig. He was just getting ready to drop it on the floor, and end its life in the usual way, when it shook itself in the spoon—spread two wet wings, and flopped onto the tablecloth. There it sat, stroking itself with its feet and stretching its wings, and Harry said: "Why, it's a tiny newt!"

The professor leaned forward before the doctor could say a word. "I'll give you half a crown for it, Harry, my lad," he said, speaking very fast; and then he picked it up carefully on his handkerchief.

"It is a new specimen," he said, "and finer than yours, Doctor."

It was a tiny lizard, about half an inch long—with scales and wings.

So now the doctor and the professor each had a specimen, and they were both very pleased. But before long these specimens began to seem less valuable. For the next morning, when the knife-boy was cleaning the doctor's boots, he suddenly dropped the brushes and the boot and the blacking, and screamed out that he was burnt.

And from inside the boot came crawling a lizard as big as a kitten, with large, shiny wings.

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