White light is refracted by the triangular prism shown in the figure below. A beam of light enters the prism along a path parallel to the prism base. The light is observed on a screen that is located $\displaystyle 10m$ away from the prism and is perpendicular to the emerging rays. How far apart on the screen are the spots of blue light ($\displaystyle n=1.528$) and red light ($\displaystyle n=1.514$)

___________________________

I'm just confused as to how you're supposed to find the distance between the spots!

I've set up the problem like so:

$\displaystyle \theta_1= 65°$

$\displaystyle \theta_2= 180-90-65= 25°$

$\displaystyle \theta_3= 16.06°$

$\displaystyle \theta_4= 33.94°$

$\displaystyle \theta_5= 58.6°$

$\displaystyle \theta_6= 130°$

Now that I've found the angles, how do I find the distance? >.<

Work below (if you care):

_________________________

For $\displaystyle \theta_3$:

$\displaystyle n_2 sin(\theta_2) = n_3 sin(\theta_3)$

$\displaystyle (1) sin(25°)= 1.528(sin(\theta_3))$, $\displaystyle \theta_3 = 16.06°$

For $\displaystyle \theta_6$:

$\displaystyle \theta_6 + 50° + 90° + 90° = 180$, $\displaystyle \theta_6 = 130°$

For $\displaystyle \theta_4$:

$\displaystyle \theta_3 +\theta_4 +\theta_6 = 180$, $\displaystyle \theta_4=33.94°$

For $\displaystyle \theta_5$:

$\displaystyle n_4 sin(\theta_4) = n_5 sin(\theta_5)$

$\displaystyle 1.528 sin(33.94°)= (1)(sin(\theta_5))$, $\displaystyle \theta_5 =58.6°$