Question

Diamonds have an index of refraction of 2.42, while fused quartz has an index of refraction of 1.46. Therefore, the speed of light in diamonds is...Select one:a. lower than that in quartz.b. greater than that in quartz. c. the same as that in quartz.d. unknown.

Answer 1

Step-by-step explanation

The refractive index of a medium (n) is equal to the speed of light (c) divided by the velocity of light through the medium (v)

`\begin{gathered} n=(c)/(v) \\ where\text{ n is the index of refraction} \\ \text{c is the speed of ligth in vacuum} \\ v\text{ is the velocity of ligth in the medium} \end{gathered}`

so

Step 1

a) for Diamons

`\begin{gathered} n=(c)/(v) \\ 2.42=(c)/(v_1) \\ isolate\text{ v}_1 \\ v_1=(c)/(2.42) \end{gathered}`

b) fuzed quarts

`\begin{gathered} n=(c)/(v) \\ 1.46=(c)/(v_2) \\ isolate\text{ v}_2 \\ v_2=(c)/(1.46) \end{gathered}`

Step 2

now,compare:

`\begin{gathered} v_(1)=(c)/(2.42) \\ v_2=(c)/(1.46) \end{gathered}`

due to c is constant, the velocity 2 is greater ( c is divide by a smaller number)

hence, the speed of light in diamonds is ..

a.lower than that in quartz.

I hope this helps you