The index of refraction for diamond is 2.42. For a diamond in the air (index of refraction = 1.00), what is the smallest angle that a light ray inside the diamond can make with a normal and completely reflect back inside the diamond (the critical angle)?

• A) 90°
• B) 45°
• C) 68°
• D) 66°
• E) 24°

To find the critical angle for light traveling from diamond to air, we can use Snell's Law, which states:

Snell's Law Formula

Snell's Law is given by:

n1 * sin(θ1) = n2 * sin(θ2)

Where:

• n1 = index of refraction of the first medium (diamond = 2.42)
• n2 = index of refraction of the second medium (air = 1.00)
• θ1 = angle of incidence (inside diamond)
• θ2 = angle of refraction (in air)

Finding the Critical Angle

The critical angle occurs when the angle of refraction (θ2) is 90°, meaning the light ray travels along the boundary. Thus, we can set θ2 to 90°:

Using Snell's Law:

2.42 * sin(θc) = 1.00 * sin(90°)

Since sin(90°) = 1, the equation simplifies to:

2.42 * sin(θc) = 1

Now, solving for sin(θc):

sin(θc) = 1 / 2.42

sin(θc) ≈ 0.4132

Next, we find θc by taking the inverse sine:

θc = sin^-1(0.4132)

Calculating this gives:

θc ≈ 24°

Final Answer

The smallest angle that a light ray inside the diamond can make with the normal and still reflect completely back inside is 24°. Therefore, the correct answer is E) 24°.