The side of a fish tank is made up of a thick parallel sided piece of glass.The refractive index for glass is 1.52.A beam of light strikes the surface of the glass at an angle of 46 degrees with rspect to the normal.What direction will the beam move in the water.Show all CALCULATIONS
The light beam is refracted twice: first going from air to glass, and then from glass to water.
Nair = 1.00 angle A1 = 46
Nglass = 1.52 A2 = ?
Nwater = 1.33 A3 = ?
Snell's Law tells you that
1.00 sin A1 = 1.52 sin A2 = 1.33 sin A3
= sin 46 = 0.7193
Therefore
Sin A2 = 0.4732 A2 = 28.3 degrees
Sin A3 = 0.5408 A3 = 32.7 degrees
Since the glass wall is a parallel slab, the angle of the beam in the water, A3, does not depend upon the index of glass, but does depend upon the index of water.
To determine the direction in which the beam of light will move in the water, we need to calculate the angle of refraction using Snell's law.
Snell's Law is given by:
n₁ * sin(θ₁) = n₂ * sin(θ₂)
Where:
n₁ is the refractive index of the medium the light is coming from (in this case, air)
θ₁ is the angle of incidence (angle at which the light strikes the boundary)
n₂ is the refractive index of the medium the light is entering (in this case, water)
θ₂ is the angle of refraction (angle at which the light bends as it enters the water)
Given:
Refractive index of glass (n₁) = 1.52
Angle of incidence (θ₁) = 46 degrees
Step 1: Convert the angle of incidence to radians
θ₁ = 46 degrees * π/180
θ₁ = 0.8028 radians
Step 2: Apply Snell's law to calculate the angle of refraction (θ₂)
n₁ * sin(θ₁) = n₂ * sin(θ₂)
1.52 * sin(0.8028) = 1.33 * sin(θ₂)
θ₂ = sin⁻¹((1.52 * sin(0.8028)) / 1.33)
θ₂ ≈ 0.808 radians
Step 3: Convert the angle of refraction to degrees
θ₂ ≈ 0.808 * 180/π
θ₂ ≈ 46.28 degrees
Therefore, the beam of light will move in the water at an angle of approximately 46.28 degrees with respect to the normal.