A ray of light passes from air through a rectangular block of glass with parallel faces 4.5cm apart at an angle of incidence of 52°
To solve this problem, we can use Snell's Law, which relates the angle of incidence (θ1), angle of refraction (θ2), and the refractive indices (n1, n2) of two mediums. Snell's Law is given by:
n1*sin(θ1) = n2*sin(θ2)
In this case, the light is passing from air (n1 ≈ 1) to glass (n2 ≈ 1.5).
Given:
- Angle of incidence (θ1) = 52°
- Distance between the parallel faces of the glass block (d) = 4.5 cm
First, we need to find the angle of refraction (θ2). Rearranging Snell's Law, we have:
sin(θ2) = (n1/n2)*sin(θ1)
sin(θ2) = (1/1.5)*sin(52°)
sin(θ2) ≈ 0.698
To find the angle of refraction (θ2), we take the inverse sine (sin^(-1)) of 0.698:
θ2 = sin^(-1)(0.698)
θ2 ≈ 43.34°
Therefore, the angle of refraction (θ2) is approximately 43.34°.
Next, we can use the angle of incidence (θ1) and the angle of refraction (θ2) to find the lateral shift (x) of the light beam inside the glass block.
x = d*tan(θ1 - θ2)
x = 4.5 cm * tan(52° - 43.34°)
x ≈ 2.66 cm
Therefore, the lateral shift (x) of the light beam inside the glass block is approximately 2.66 cm.
To find the angle of refraction and the path of the ray inside the glass, you can use Snell's law. Snell's law relates the angles of incidence and refraction to the indices of refraction of the two mediums involved.
1. Determine the indices of refraction:
- The index of refraction of air (n_air) is approximately 1.
- The index of refraction of glass (n_glass) can vary, but for simplicity, let's assume it is 1.5.
2. Convert the angle of incidence to radians:
- Angle of incidence (θ) = 52°
- Angle in radians (θ_radians) = θ × π / 180
- θ_radians = 52° × π / 180 ≈ 0.907 radians
3. Apply Snell's law to find the angle of refraction:
- Snell's law states: n_air × sin(θ_air) = n_glass × sin(θ_glass), where θ_air is the angle of incidence and θ_glass is the angle of refraction.
- Rearrange the equation to solve for θ_glass: θ_glass = arcsin((n_air / n_glass) × sin(θ_air))
- Substituting the known values: θ_glass ≈ arcsin((1 / 1.5) × sin(0.907)).
4. Calculate the angle of refraction:
- Using a calculator or trigonometric table, evaluate the arcsin term to get θ_glass.
- The approximate value of θ_glass will depend on the specific numbers used.
5. Determine the path of the ray inside the glass:
- The light ray will travel in a straight path through the glass block, since the faces of the block are parallel.
- The path of the ray will be governed by the angle of refraction found in step 4.
Remember to calculate the values numerically to get the precise results.