Answer:
(a). The angle of refraction is 19.26°.
(b). That is proved that the rays in air on either side of the glass are parallel to each other
Explanation:
Given that,
Angle of incidence = 30.0°
Index of reflection of glass = 1.52
(a). We need to calculate the angle of refraction for the ray inside the glass
Using snell's law


Put the value into the formula



(b). We know that,
The incident ray and emerging ray is equal then the ray will be parallel.
We need to prove that the rays in air on either side of the glass are parallel to each other
Using formula for emerging ray


Put the value into the formula



So, 
This is proved.
Hence, (a). The angle of refraction is 19.26°.
(b). That is proved that the rays in air on either side of the glass are parallel to each other
Answer:
Distance: 21 yd, displacement: 15 yd, gain in the play: 12 yd
Explanation:
The distance travelled by Sam is just the sum of the length of each part of Sam's motion, regardless of the direction. Initially, Sam run from the 3 yd line to the 15 yd line, so (15-3)=12 yd. Then, he run also 9 yd to the right. Therefore, the total distance is
d = 12 + 9 = 21 yd
The displacement instead is a vector connecting the starting point with the final point of the motion. Sam run first 12 yd straight ahead and then 9 yd to the right; these two motions are perpendicular to each other, so we can find the displacement simply by using Pythagorean's theorem:

Finally, the yards gained by Sam in the play are simply given by the distance covered along the forward-backward direction only. Since Sam only run from the 3 yd line to the 15 yd line along this direction, then the gain in this play was
d = 15 - 3 = 12 yd