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Diamonds sparkle because light that enters the diamond is reflected back to an observer - Scottish Highers Physics - Question 11 - 2019

Question 11

Diamonds sparkle because light that enters the diamond is reflected back to an observer. (a) A ray of monochromatic light is incident on a diamond at an angle of 49... show full transcript

Worked Solution & Example Answer:Diamonds sparkle because light that enters the diamond is reflected back to an observer - Scottish Highers Physics - Question 11 - 2019

Step 1

A ray of monochromatic light is incident on a diamond at an angle of 49°. The refractive index of diamond for this light is 2.42. Calculate the angle of refraction θ.

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Answer

To calculate the angle of refraction, we can use Snell's Law, which states:

$n_1 \sin(\theta_1) = n_2 \sin(\theta_2)$

Where:
n₁ = refractive index of air = 1
n₂ = refractive index of diamond = 2.42
θ₁ = angle of incidence = 49°

Substituting the known values, we get:

$1 \sin(49°) = 2.42 \sin(\theta_2)$

Rearranging gives:

$\sin(\theta_2) = \frac{\sin(49°)}{2.42}$

Calculating \sin(49°): $\sin(49°) ≈ 0.7547$

Thus,

$\sin(\theta_2) = \frac{0.7547}{2.42} ≈ 0.3116$

Now, finding θ₂: $\theta_2 ≈ \sin^{-1}(0.3116) ≈ 18.2°$

Therefore, the angle of refraction θ is approximately 18.2°.

Step 2

Calculate the critical angle of the diamond for this light.

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Answer

The critical angle (θ_c) is calculated using the formula:

$\theta_c = \sin^{-1}\left(\frac{n_2}{n_1}\right)$

Where:

n₂ is the refractive index of diamond (2.42)
n₁ is the refractive index of air (1)

Substituting the values:

$\theta_c = \sin^{-1}\left(\frac{2.42}{1}\right)$

Since we need the sine to be less than or equal to 1, we find:

$\theta_c = \sin^{-1}(1) = 90°$ (not practically reachable) For diamond, we will use the following expression:

$\theta_c = \sin^{-1}(\frac{1}{2.42})$

Calculating: $\theta_c ≈ 24.4°$

Thus, the critical angle of the diamond is approximately 24.4°.

Step 3

State whether the sample of moissanite sparkles more or less than the diamond. You must justify your answer.

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Answer

Moissanite sparkles more than diamond.

This is because the refractive index of moissanite is greater than that of diamond, which means:

The critical angle for moissanite is smaller than that for diamond.
Total internal reflection is more likely to happen in moissanite, leading to increased brilliance and sparkle.

In conclusion, the higher refractive index results in enhanced sparkle.

Diamonds sparkle because light that enters the diamond is reflected back to an observer - Scottish Highers Physics - Question 11 - 2019

Worked Solution & Example Answer:Diamonds sparkle because light that enters the diamond is reflected back to an observer - Scottish Highers Physics - Question 11 - 2019

A ray of monochromatic light is incident on a diamond at an angle of 49°. The refractive index of diamond for this light is 2.42. Calculate the angle of refraction θ.

Calculate the critical angle of the diamond for this light.

State whether the sample of moissanite sparkles more or less than the diamond. You must justify your answer.

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