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.
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°
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