Final answer:
a) The angle of refraction is approximately 7.85°. b) The angle of incidence should be approximately 35.20° to achieve an angle of refraction not greater than 45°. c) The critical angle is approximately 48.60°.
Step-by-step explanation:
a) To find the angle of refraction, we can use Snell's Law, which states that the ratio of the sine of the angle of incidence to the sine of the angle of refraction is equal to the ratio of the refractive indices of the two media. In this case, the angle of incidence is 10° and the refractive index of water is 1.3. We can rearrange and solve for the angle of refraction:
sin(angle of incidence) / sin(angle of refraction) = refractive index of water / refractive index of air
sin(10°) / sin(angle of refraction) = 1.3 / 1
sin(angle of refraction) = sin(10°) / 1.3
angle of refraction = sin-1(sin(10°) / 1.3)
angle of refraction ≈ 7.85°
b) To find the angle of incidence for an angle of refraction not greater than 45°, we can use Snell's Law again. Let's assume the angle of refraction is 45°. We can rearrange and solve for the angle of incidence:
sin(angle of incidence) / sin(45°) = refractive index of water / refractive index of air
sin(angle of incidence) = sin(45°) / 1.3
angle of incidence = sin-1(sin(45°) / 1.3)
angle of incidence ≈ 35.20°
c) The critical angle is the angle of incidence at which the angle of refraction is 90°. To find the critical angle, we can use Snell's Law:
sin(critical angle) = refractive index of air / refractive index of water
sin(critical angle) = 1 / 1.3
critical angle = sin-1(1 / 1.3)
critical angle ≈ 48.60°