A light ray strikes a flat, L = 3.7 cm thick block of glass of refractive index 1.47 in the attached figure, at an angle of È = 340 with the normal.
Calculate the lateral shift of the light ray, d.
To calculate the lateral shift of the light ray, we can use the formula:
d = L * tan(θ)
Where:
- d is the lateral shift of the light ray
- L is the thickness of the glass block
- θ is the angle of incidence with respect to the normal
Given:
- L = 3.7 cm
- refractive index (n) of glass = 1.47
- angle of incidence (θ) = 340 degrees
First, we need to convert the angle from degrees to radians:
θ_radians = θ * (π/180)
= 340 * (π/180)
= 5.94 radians
Next, we need to find the angle of refraction (φ) using Snell's Law:
n1 * sin(θ) = n2 * sin(φ)
Here, n1 is the refractive index of the medium from which the light is coming (usually air, so n1 = 1), and n2 is the refractive index of the glass (given as 1.47).
sin(φ) = (n1 / n2) * sin(θ)
= (1 / 1.47) * sin(θ)
= (1 / 1.47) * sin(θ_radians)
Now, we can calculate the lateral shift using:
d = L * tan(φ)
d = L * tan(φ_radians)
= L * tan( arctan( sin(φ) ) )
= L * tan( arctan( (1 / 1.47) * sin(θ_radians) ) )
Substituting the given values:
d = 3.7 cm * tan( arctan( (1 / 1.47) * sin(5.94) ) )
Using a calculator, compute the value of the expression inside the tangent function, then calculate the tangent function and multiply by the thickness L to find the lateral shift (d). The result will be in cm.