Which of the following is the critical angle for light passing from diamond into air? Note: ndiamond=2.42 and nair=1.

Group of answer choices

48.81°

24.41°

1.00°

2.42°

1 answer

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°