Question

The critical angle will be largest when light goes from ______.

Options

• water to air

• glass to air

• glass to water

• diamond to air

Answer 1

The critical angle will be largest when light goes from glass to water.

Explanation:

The critical angle is largest when light goes from a medium with a lower refractive index to one with a higher refractive index ratio closer to 1.

Given options:

Water to air (n_water ≈ 1.33, n_air = 1.00)

Glass to air (n_glass ≈ 1.5, n_air = 1.00)

Glass to water (n_glass ≈ 1.5, n_water ≈ 1.33)

Diamond to air (`"n"_"diamond"` ≈ 2.42, n_air = 1.00)

The critical angle C is given by:

sin C = `n_("less dense")/(n_"denser")`

Therefore, the critical angle is largest for glass to water since:

sin C = `1.33/1.5`

= 0.8867

⇒ C = 62.5°

Compared to water to air (48.8°), glass to air (41.1°), and diamond to air (smaller because diamond’s refractive index is much higher).

The critical angle is larger when the ratio of refractive indices is closer to 1. Glass to water has the closest refractive indices, giving the largest critical angle.