To find the critical angle for light passing from diamond to air, you can use Snell's law and the formula for the critical angle, which is given by:
\[ \sin(\theta_c) = \frac{n_2}{n_1} \]
where:
- \(\theta_c\) is the critical angle,
- \(n_1\) is the refractive index of the material light is coming from (diamond), and
- \(n_2\) is the refractive index of the material light is entering (air).
In this case, the refractive index for diamond (\(n_1\)) is 2.42, and for air (\(n_2\)) it is 1.00.
Now, we can substitute these values:
\[ \sin(\theta_c) = \frac{1.00}{2.42} \]
Calculating that gives:
\[ \sin(\theta_c) \approx 0.4132 \]
Next, we find the critical angle \(\theta_c\) by taking the inverse sine (arcsin) of this value:
\[ \theta_c \approx \arcsin(0.4132) \approx 24.41° \]
Thus, the critical angle for light passing from diamond to air is approximately 24.41°.
The correct answer is:
24.41°