Final answer:
The light strikes the coral with the same wavelength as it had in air, which is 415 nm. The velocity of the light when it strikes the coral is approximately 0.748c in terms of c.
Step-by-step explanation:
When light passes from one medium to another, it changes its wavelength and velocity. To find the wavelength of the light when it strikes the coral, we can use Snell's law:
n1 * sin(theta1) = n2 * sin(theta2)
Here, n1 is the index of refraction of the boat (1.000), theta1 is the angle of incidence (which is 0 since the light is shining perpendicular to the water surface), n2 is the index of refraction of the water (1.336), and we need to solve for theta2. Rearranging the equation:
sin(theta2) = (n1 / n2) * sin(theta1)
Plugging in the values:
sin(theta2) = (1.000 / 1.336) * sin(0)
sin(theta2) = 0
Since the sine of theta2 is 0, it means that theta2 is 0 as well. This means that the light does not refract and continues to travel in a straight line when it enters the water. Therefore, the wavelength of the light does not change when it strikes the coral. It remains 415 nm, which is violet light.
To find the velocity of the light when it strikes the coral in terms of c (the speed of light in vacuum), we can use the equation:
v = c / n
Here, v is the velocity of light in the water, c is the speed of light in vacuum (which is 1.00c), and n is the index of refraction of the water (1.336). Plugging in the values:
v = 1.00c / 1.336
v = 0.748c
Therefore, the velocity of the light when it strikes the coral is approximately 0.748c in terms of c.