Identical rays of light in air are refracted upon entering three transparent materials:
A) water, (where the speed of light is 0.75c);
B) ethyl alcohol (speed 0.7c); and
C) crown glass (speed 0.6c).
Rank the materials according to how much the light ray bends toward the normal, from most bending to least bending.

Explanation:

for us to rank them we need to calculate the angle of refraction for the various materials. The angle of refraction is the angle between the refracted ray and the normal.

refractive index(n) = velocity of light in air/ velocity of light in medium

refractive index (n) = sini/sinr

lets equate the right side of both equations.

we will assume 30 degree as the angle of incidence for all materials.

(a) water

sinr = 0.75c/c *sin30

sinr = 0.375

r= arcsin0.375

r=22.02°

(b) ethyl alcohol

sinr = 0.7c/c *sin30

sinr = 0.35

r= arcsin0.35

r=20.49°

(c) crown glass

sinr = 0.6c/c *sin30

sinr = 0.3

r= arcsin0.35

r=17.46°

it is observed that the angle of refraction decreases as the velocity of light in glass decreases.

ranking the materials  according to how much the light ray bends toward the normal, from most bending to least bending we have;

Crown glass > ethyl alcohol> water

2b2t

explanation:

2b2t

see the picture for the vector

the magnitude of the vector by pythagorean theorem

r = √( (-10)^2 + (3)^2 ) = √109

magnitude = √109 units

the direction angle between vector and x-axis is

tan^(-1)(3/10) = 16.699

so the direction is approximately 16.7 degrees north of west