A very narrow beam of white light is incident at 47.50° onto the top surface of a rectangular block of flint glass 13.6 cm thick. The indices of refraction of the glass for red and violet light are 1.649 and 1.678, respectively.

1. Calculate dispersion angle...Figured this out already.

2. How wide is the beam when it reaches the bottom of the block, as measured along the bottom surface of the block?

3. When the rainbow-colored beam emerges from the bottom of the block, the exiting rays of light are once again parallel. Calculate the distance between the exiting red and violet rays (i.e., the thickness of the rainbow).

Any help with 2 and 3 would greatly be appreciated.
Thanks

2. you know the dispersion angle. YOu will have to use trig to find width at trig bottom. Draw the figure, label the paths, and I assume you know how thick the glass is.

3. Same principle as 2.

To calculate questions 2 and 3, we can use Snell's Law and the concept of refraction.

2. To calculate the width of the beam when it reaches the bottom of the block, as measured along the bottom surface of the block, we need to find the angle of refraction at the bottom surface.

Here's how you can do it:
- Using Snell's Law, we can relate the angle of incidence and angle of refraction:
n1 * sin(theta1) = n2 * sin(theta2),
where n1 and n2 are the refractive indices, theta1 is the angle of incidence, and theta2 is the angle of refraction.
- In this case, the light beam is incident on the top surface of the block, so we can use the angle of incidence calculated in question 1.
- Since we want to find the width of the beam along the bottom surface, we need to find the angle of refraction at the bottom surface.
- Rearrange the Snell's Law equation to solve for sin(theta2):
sin(theta2) = (n1 * sin(theta1)) / n2.
- Substitute the values: n1 = 1 (air), sin(theta1) = sin(47.50°), and n2 is the refractive index for red light (1.649) or violet light (1.678).
- Calculate sin(theta2) for both red and violet light.
- Finally, use the relation: width = thickness * tan(theta2).
Substitute the values: thickness = 13.6 cm and theta2 calculated for both red and violet light, to find the width of the beam.

3. To calculate the distance between the exiting red and violet rays (i.e., the thickness of the rainbow), we can use the fact that the rays are once again parallel.
- When the rays emerge from the bottom of the block, they are parallel because there is no further refraction at the interface between the block and air.
- So, the distance between the exiting red and violet rays is the same as the distance between the entering red and violet rays at the top surface of the block.
- Using Snell's Law, we can calculate the angle of refraction at the top surface and then calculate the distance using the same method as question 2.

By following these steps, you should be able to calculate the width of the beam when it reaches the bottom of the block (question 2) and the distance between the exiting red and violet rays (question 3).