# which statement is true if the refractive index of a medium a is greater than that of medium b

Question

which statement is true if the refractive index of a medium a is greater than that of medium b

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1 year 2021-09-04T22:13:23+00:00 2 Answers 4 views 0

b.

Explanation:

B) total internal reflection is possible when light travels from medium a to medium b.

Explanation:

The index of refraction of a medium is the ratio between the speed of light in a vacuum (c) and the speed of light in that medium (v):

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

When a ray of light crosses the interface between two mediums, it undergoes refraction, which means it is is bent and its speed changes, according to Snell’s law:

$$n_1 sin \theta_1 = n_2 sin \theta_2$$

where

$$n_1,n_2$$ are the index of refraction of medium 1 and 2

$$\theta_1, \theta_2$$ are the angle of incidence and of refraction

We can rewrite the equation as

$$sin \theta_2 = \frac{n_1}{n_2}sin \theta_1$$

From this equation, we observe that if $$n_1>n_2$$, then the ratio $$\frac{n_1}{n_2}>1$$; however, $$sin \theta_2$$ cannot be larger than 1. This means that in this case, there will be a maximum value of $$\theta_1$$ above which refraction no longer occurs: in that situation, the light coming from the 1st medium is entirely reflected inside the 1st medium, and this phenomenon is called total internal reflection.

The value of the critical angle above which total internal reflection occurs is

$$\theta_c = sin^{-1}(\frac{n_2}{n_1})$$

In this situation, we have:

$$n_A > n_B$$ (index of refraction of A is larger than index of refraction of B)

Also, the index of refraction of air is 1.00, so it is lower than the index of refraction of every medium:

$$n_A > n_B > n_{air}$$

Since total internal reflection occurs only if the index of refraction of medium 1 is higher than that of medium 2, the correct statements are:

B) total internal reflection is possible when light travels from medium a to medium b.