You shine your laser pointer through the flat glass side of a rectangular aquarium at an angle of incidence of 45 degrees. The index of refraction of this type of glass is 1.55.
A. At what angle from the normal does the beam from the laser pointer enter the water inside the aquarium?
B. Does your answer to part a depend on the index of refraction of the glass?
The answer is 32.1. But I don't know how to get the answer. Please Help.
n1sinQ1 = n2sinQ2 for air/glass interface
Angle = 27degrees which is sinQ2
n2sinQ2 = n3sinQ3 for glass/water interface
To find the angle at which the beam from the laser pointer enters the water inside the aquarium (part A), we can start by considering how the light is refracted at the glass-water interface. We'll also need to use Snell's Law, which relates the angles of incidence and refraction and the refractive indices of the two media.
Let's denote:
θ1 = angle of incidence (from the normal) in glass
θ2 = angle of refraction (from the normal) in water
n1 = refractive index of glass (1.55)
n2 = refractive index of water (approximately 1.33)
According to Snell's Law:
n1 sin(θ1) = n2 sin(θ2)
Since we know the angle of incidence in glass is 45 degrees, we can substitute those values:
1.55 sin(45°) = 1.33 sin(θ2)
Now we can solve for θ2 by rearranging the equation:
sin(θ2) = (1.55/1.33) sin(45°)
θ2 ≈ arcsin((1.55/1.33) sin(45°))
To find the approximate value of θ2, we can substitute the given numbers:
θ2 ≈ arcsin((1.16) * 0.7071)
Using a calculator, we can find:
θ2 ≈ 49.5°
Therefore, the beam from the laser pointer enters the water inside the aquarium at an angle of approximately 49.5 degrees from the normal.
Now, let's move on to part B. Does the answer to part A depend on the index of refraction of the glass?
Yes, the answer to part A does depend on the index of refraction of the glass. The refractive index of a medium determines how much the light is bent or refracted when it passes from one medium to another. In this case, the angle of refraction in water depends on the refractive index of the glass, which is why we needed to know it in order to calculate θ2. If the glass had a different refractive index, the angle at which the beam enters the water would change.