Question

Light consisting of a mixture of red and blue light enters a 40°, 70°, 70° prism along a line parallel to the side opposite the 40° vertex. the index of refractio n of the prism material for blue light is 1.530, and for red light it is 1.525. what is the angle between the two emergin g beams of light?

Answer 1

To find the angle between the two emerging beams of light, use Snell's law to calculate the angle of refraction for each color of light, and then subtract the two angles to find the angle between the two emerging beams.

Step-by-step explanation:

To find the angle between the two emerging beams of light, we need to use Snell's law, which states that the ratio of the sines of the angles of incidence and refraction is equal to the ratio of the indices of refraction.

1. First, find the angle of refraction for each color of light by using Snell's law: sin(angle of incidence) / sin(angle of refraction) = index of refraction.
2. Next, subtract the two angles of refraction to find the angle between the two emerging beams.

Given that the index of refraction for blue light is 1.530 and for red light is 1.525, you can now calculate the angle between the two emerging beams of light.

Answer 2

this is actually a simple problem of trigonometry

first take a look at the picture
you need to understand that the incident beam of light meets the left side of the prism at a 70° angle wich makes angle v = 20°
then that left normal and right normal make an 140° angle (those normals with the upper corner of the prism form a 4-side polygon with the sum of all angles 360°, two of its angles are 90° and the upper one is 40°, therefore the 4th angle is 360-90-90-40=140)

ok, now comes the only physics part of the problem
you only need to know the refractive index formula
n(air)*sinv = n(prism for blue)*sinb
n(air)*sinv = n(prism for red)*sinr

so we have
sinv = 1.530*sinb => sinb= sin20°/1.530 = 0.342/1.530 = 0.223 => b=12.92°
sinv = 1.525*sinr => sinr = sin20°/1.525 = 0.342/1.525 = 0.224 => r=12.96°

now, we know that the sum of a triangle angles is 180° so r+r1+140=180
therefore r1=27.04
same way we get b1 = 24.08

then again we apply the refractive index formula
and we get
sinr2 = 1.525*sin27.04° = 1.525*0.455 = 0.693 => r2 = 43.86°
sinb2 = 1.530*sin24.08° = 1.530*0.408 = 0.624 => b2= 38.62°

now the angle between blue and red rays is r2-b2 = 5.24°