Match the indices of refraction with the corresponding effects on the waves.
Select all that apply to the lower index of refraction.
A) waves bend towards the normal
B) waves speed up
C) waves bend away from the normal
D) waves slow down

B) waves speed up

C) waves bend away from the normal

Explanation:

The index of refraction of a material is the ratio between the  speed of light in a vacuum and the speed of light in that medium:

where

c is the speed of light in a vacuum

v is the speed of light in the medium

We can re-arrange this equation as:

So from this we already see that if the index of refraction is lower, the speed of light in the medium will be higher, so one correct option is

B) waves speed up

Moreover, when light enters a medium bends according to Snell's Law:

where

are the index of refraction of the 1st and 2nd medium

are the angles made by the incident ray and refracted ray with the normal to the interface

We can rewrite the equation as

So we see that if the index of refraction of the second medium is lower (), then the ratio is larger than 1, so the angle of refraction is larger than the angle of incidence:

This means that the wave will bend away from the normal. So the other correct option is

C) waves bend away from the normal

anchor = archer //

we have been given a quadratic function and we need to restrict the domain such that it becomes a one to one function.

we know that vertex of this quadratic function occurs at (5,2).

further, we know that range of this function is .

if we restrict the domain of this function to either or , it will become one to one function.

let us know find its inverse.

upon interchanging x and y, we get:

let us now solve this function for y.

hence, the inverse function would be if we restrict the domain of original function to and the inverse function would be if we restrict the domain to .