An equilateral prism of silica flint glassis used to refract white light. The indexof refraction of silica flint is 1.66 forviolet light and 1.62 for red light.
What is the angle of separation between
the violet and red ends of the rainbow
produced when the ray of white light is
incident at an angle of 50.0° with
respect to the normal?
From what i understand in this question, white light goes from air through the prism which splits it into red and violet. the question is asking about the angle between red and violet when it comes out in the air from the prism.
i used snells law to find the angle of refraction in the prism first.
going from air to prism
red => 1sin50 = 1.62 sin (theta)
theta (red) = 28.22
violet => 1 sin50 = 1.66 sin (theta)
theta (violet) = 27.48
i tried to use these angles to find the refraction angles from prism to air which gives me 50 again and sounds wrong.
not sure how to go about this problem.
please help.
thankyou
There are are two refractions, you will have to draw a diagram and figure the effect of each refraction.
http://www.physicsclassroom.com/Class/refrn/u14l4a.cfm
PRIMARY RAINBOW: Combine φ=4r−2i with Snell's Law to express the angle φ as a function of i and n only.
(a) Evaluate φ(i,n) for the following values (give your answers in degrees):
a.1) i=3∘, n=1.35
a.2) i=46∘, n=1.3
To find the angle of separation between the violet and red ends of the rainbow, we need to use the concept of dispersion of light.
The dispersion of light occurs when different colors travel at different speeds through a medium, such as a prism, causing them to change direction by different amounts. This results in the separation of white light into its constituent colors.
In this case, we have an equilateral prism of silica flint glass. The index of refraction for violet light is 1.66, and for red light, it is 1.62.
To begin, we can calculate the angle of deviation for each color of light using Snell's Law. Snell's Law states that the ratio of the sine of the angle of incidence to the sine of the angle of refraction is equal to the ratio of the indices of refraction of the two media involved:
n1 * sin(angle of incidence) = n2 * sin(angle of refraction)
For violet light:
n1 (violet) = 1.66
n2 (air) = 1.00 (approximating air as having an index of refraction of 1.00)
angle of incidence = 50.0° (given)
We can rearrange the formula to solve for the angle of refraction:
sin(angle of refraction, violet) = (n1 * sin(angle of incidence)) / n2
sin(angle of refraction, violet) = (1.66 * sin(50.0°)) / 1.00
angle of refraction, violet ≈ arcsin(1.66 * sin(50.0°) / 1.00)
Similarly, for red light:
n1 (red) = 1.62
angle of refraction, red ≈ arcsin(1.62 * sin(50.0°) / 1.00)
Once we have the angles of refraction for both violet and red light, we can find the angle of separation between the two colors by subtracting one from the other:
angle of separation = angle of refraction, violet - angle of refraction, red
Finally, we can plug in the values and calculate the angle of separation. Keep in mind to use a scientific calculator or a tool capable of calculating trigonometric functions accurately.