Question

A light ray in glass (n = 1.50) strikes an unknown material with an angle of incidence of 45.0°. The angle of refraction in this material is measured to be 67.0°. What is the index of refraction of this material

Answer 1

The index of refraction of the unknown material is approximately 1.15, which is calculated using Snell's Law given the light ray's angle of incidence and angle of refraction.

Step-by-step explanation:

To find the index of refraction of the unknown material where a light ray in glass (n = 1.50) strikes with an angle of incidence of 45.0° and the angle of refraction is 67.0°, we use Snell's Law:

Snell's Law states that n1 × sin(θ1) = n2 × sin(θ2), where:

• n1 is the index of refraction for the first medium (glass in this case).
• θ1 is the angle of incidence.
• n2 is the index of refraction for the unknown material.
• θ2 is the angle of refraction.

Plugging in the values:

1.50 × sin(45.0°) = n2 × sin(67.0°)

Calculate the left side:

1.50 × 0.7071 ≈ 1.0607

Now solve for n2:

n2 = 1.0607 / sin(67.0°)

n2 ≈ 1.0607 / 0.9219

n2 ≈ 1.15

The index of refraction of the unknown material is approximately 1.15.