For a piece of glass n(red)= 1.635 and n(blue)= 1.689. The respective wavelengths are 680nm (red) and 430nm (blue). Find the angle between these two colors of light in the glass if they were originally in a white light beam in air incident on the glass at an angle of 44.

To find the angle between the red and blue colors of light in the glass, we can use Snell's law and the formula for calculating the angle of refraction.

Snell's law states that the ratio of the sines of the angles of incidence and refraction is equal to the ratio of the velocities of light in the two mediums. In our case, the mediums are air (where the white light beam is incident) and glass.

The formula for calculating the angle of refraction is given by:

sin(θ2) = (n1/n2) * sin(θ1)

Where:
θ2 is the angle of refraction in the glass,
θ1 is the angle of incidence in air,
n1 is the refractive index of air, and
n2 is the refractive index of glass.

Given:
n(red) = 1.635
n(blue) = 1.689
θ1 = 44 degrees

First, we need to calculate the angle of refraction for each color by plugging the values into the formula.

For red light:
n1/n2 = sin(θ1)/sin(θ2)
1.000/1.635 = sin(44)/sin(θ2)
sin(θ2) = (1.635/1.000) * sin(44)
sin(θ2) = 1.635 * sin(44)

Now, we can use the inverse sine (or arcsin) function to find the value of θ2.

θ2 = arcsin(1.635 * sin(44))

Repeat the same process for blue light:

n1/n2 = sin(θ1)/sin(θ2)
1.000/1.689 = sin(44)/sin(θ2)
sin(θ2) = (1.689/1.000) * sin(44)
sin(θ2) = 1.689 * sin(44)

θ2 = arcsin(1.689 * sin(44))

Finally, subtract the angle of refraction for red light from the angle of refraction for blue light to find the angle between them:

Angle between red and blue light in the glass = θ2(blue) - θ2(red)

Please note that the final result will depend on the accuracy of the input values and the accuracy of the calculations.