A ray of sunlight is passing from diamond into crown glass; the angle of incidence is 36.00°. The indices of refraction for the blue and red components of the ray are: blue (ndiamond = 2.444, ncrown glass = 1.531), and red (ndiamond = 2.410, ncrown glass = 1.520). Determine the angle between the refracted blue and red rays in the crown glass. Give your answer to two significant figures.

Question

A ray of sunlight is passing from diamond into crown glass; the angle of incidence is 36.00°. The indices of refraction for the blue and red components of the ray are: blue (ndiamond = 2.444, ncrown glass = 1.531), and red (ndiamond = 2.410, ncrown glass = 1.520). Determine the angle between the refracted blue and red rays in the crown glass. Give your answer to two significant figures.

Answer 1

To determine the angle between the refracted blue and red rays in the crown glass, 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 of the two media:

n1 * sin(theta1) = n2 * sin(theta2)

where:
n1 = index of refraction of the initial medium (diamond)
n2 = index of refraction of the final medium (crown glass)
theta1 = angle of incidence
theta2 = angle of refraction

Let's calculate the angle of refraction for both the blue and red components of the ray separately.

For the blue component:
n1 = 2.444 (index of refraction of diamond)
n2 = 1.531 (index of refraction of crown glass)
theta1 = 36.00° (angle of incidence)

Using Snell's law:
2.444 * sin(36.00°) = 1.531 * sin(theta2_blue)

Rearranging the equation:
sin(theta2_blue) = (2.444 * sin(36.00°)) / 1.531

Calculating sin(theta2_blue):
sin(theta2_blue) ≈ 0.6755

Now, let's calculate the angle of refraction for the red component:
n1 = 2.410 (index of refraction of diamond)
n2 = 1.520 (index of refraction of crown glass)
theta1 = 36.00° (angle of incidence)

Using Snell's law:
2.410 * sin(36.00°) = 1.520 * sin(theta2_red)

Rearranging the equation:
sin(theta2_red) = (2.410 * sin(36.00°)) / 1.520

Calculating sin(theta2_red):
sin(theta2_red) ≈ 0.6777

Now we have sin(theta2_blue) ≈ 0.6755 and sin(theta2_red) ≈ 0.6777.

To find the angle between the refracted blue and red rays in the crown glass, we can use the arcsine function:

angle = arcsin |sin(theta2_blue) - sin(theta2_red)|

Calculating the angle:
angle ≈ arcsin |0.6755 - 0.6777|

angle ≈ arcsin |0.0022|

angle ≈ 0.0022° (rounded to two significant figures)

Therefore, the angle between the refracted blue and red rays in the crown glass is approximately 0.0022°.