Question

Help with these questions please?

Answer 1

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.