Three
The ray of light will come out of the glass at 90 degrees to the normal. What goes in is called the critical angle. At 90 degrees the ray will reflect rather than refract. This is just for interest.
Formula
n2 * sin(θ2) = n1* sin(θ1)
Givens
θ2 = 90 degrees
n2 = 1
n1 = ?
θ1 = 43.6
Solution
n1 * sin(43.6) = 1 * 1
n1 = 1/sin(43.6)
n1 = 1/0.6896
n1 = 1.45
Four
This problem is very instructive. It uses a little known trick so that you don't have to know the exact speed of light of one of the speeds. The other speed is compared to it. You could do it the long way and figure out the speeds in crown glass from air to the crown glass, and do the same thing with the other color. That would work. An easier way is not to bother. Call the speed of one of the colors = 1. Is the other speed greater or less than 1? We'll see.
The next thing you have to realize is that the speed is going to be highest for either red or violet. That's because n is highest for violet and lowest for red. The intermediate colors don't matter. So the answer is either A or B.
They have n's between violet and red and so they will not be an answer. That means you can eliminate green and yellow (answers C and D).
Formula
v1/v2 = n2/n1
Givens
v1 = 1 (we'll say this is red)
v2 = ? (this is violet)
n2 = 1.62 for red. This is probably not exact, but it does not have to be. You just have to notice that violet is higher
n1 = 1.65 for violet. So you are trying to solve the relative speed of v2.
Solution
v1/v2 = n2/n1
1/v2 = 1.65/1.62 Cross multiply
1.65 * v2 = 1 * 1.62 Divide by 1.65
v2 = 1.62/1.65
v2 = 0.98
Conclusion.
The speed of violet is going to be slower than the speed of red.
Rule: the higher the index of refraction, the lower the speed.
Answer: red has the greater speed.