1. Critical angle condition for green light

When light goes from a denser medium (water) to a rarer medium (air), the critical angle $\theta_c$ for a given color satisfies

$\sin \theta_c = \frac{n_{\text{air}}}{n_{\text{water}}} \approx \frac{1}{n_{\text{water}}}$

For green light, the incident angle is given to be exactly its critical angle. Hence for green,

$r = 90^\circ$

where $r$ is the angle of refraction in air.

2. Use dispersion: refractive index depends on color

In water, refractive index is larger for higher frequency (smaller wavelength) light.

So among visible colors:

• Violet/blue: higher frequency $\Rightarrow$ larger refractive index
• Red/yellow: lower frequency $\Rightarrow$ smaller refractive index

Thus,

$n_{\text{violet}} > n_{\text{green}} > n_{\text{red}}$

3. How critical angle changes with refractive index

Since

$\sin \theta_c = \frac{1}{n}$

if $n$ is larger, then $\theta_c$ is smaller.

Therefore:

• Higher frequency than green $\Rightarrow$ larger $n$ $\Rightarrow$ smaller critical angle
• Lower frequency than green $\Rightarrow$ smaller $n$ $\Rightarrow$ larger critical angle

So,

$\theta_{c,\text{high freq}} < \theta_{c,\text{green}} < \theta_{c,\text{low freq}}$

4. Compare the actual incident angle with critical angles of other colors

The actual incident angle is

$i = \theta_{c,\text{green}}$

For colors with frequency less than green:

Their critical angle is larger than green's, so

$i < \theta_c$

Hence they refract out into air.

For colors with frequency more than green:

Their critical angle is smaller than green's, so

$i > \theta_c$

Hence they undergo total internal reflection and do not emerge into air.

Green itself emerges at

$r = 90^\circ$

5. Check options

• A: False. Only green emerges at $90^\circ$, not the whole spectrum.
• B: True. Colors with frequency less than green have larger critical angles, so they emerge into air.
• C: False. Higher-frequency colors undergo total internal reflection.
• D: False. Not the entire spectrum emerges; only lower-frequency colors than green emerge, and green at $90^\circ$.

6. Final answer

The correct option is:

$\boxed{\text{B}}$

This matches the stored correct answer.