By what length is a light ray displaced after passing through a 4.7 cm thick sheet of material (n=1.38) with an incident angle of theta = 33.5°.
To find the length by which a light ray is displaced after passing through a material, we can use the concept of refraction. The displacement is given by the formula:
Displacement = thickness of material x tan(theta)
Let's calculate the displacement step by step:
Step 1: Convert the incident angle from degrees to radians.
To convert from degrees to radians, we use the formula: radians = degrees x pi/180.
theta = 33.5° = 33.5 x (pi/180) = 0.5854 radians.
Step 2: Calculate the displacement.
Displacement = 4.7 cm x tan(0.5854)
Using a calculator, we find: Displacement ≈ 2.912 cm.
Therefore, the light ray is displaced by approximately 2.912 cm after passing through the 4.7 cm thick sheet of material with an incident angle of 33.5°.
To find the displacement length of a light ray passing through a material, we can use the formula:
Displacement length = Thickness of the material * (tan(theta_exit) - tan(theta_incident))
Here, the thickness of the material is given as 4.7 cm and the incident angle is given as 33.5°. We need to find the exit angle (theta_exit) to calculate the displacement length.
To find the exit angle, we can use Snell's Law, which states:
n1 * sin(theta_incident) = n2 * sin(theta_exit)
Where:
- n1 is the refractive index of the initial medium (air, generally around 1.00),
- n2 is the refractive index of the material,
- theta_incident is the incident angle, and
- theta_exit is the exit angle.
In this case, n1 is approximately 1.00 and n2 is given as 1.38.
First, we can calculate the exit angle (theta_exit) using Snell's law:
n1 * sin(theta_incident) = n2 * sin(theta_exit)
1.00 * sin(33.5°) = 1.38 * sin(theta_exit)
sin(theta_exit) = (1.00 * sin(33.5°)) / 1.38
sin(theta_exit) ≈ 0.694
Taking the inverse sine (or arcsine) of both sides, we find:
theta_exit ≈ arcsin(0.694)
theta_exit ≈ 45.4°
Now, we can substitute the values into the displacement length formula:
Displacement length = (Thickness of the material) * (tan(theta_exit) - tan(theta_incident))
= (4.7 cm) * (tan(45.4°) - tan(33.5°))
Using a scientific calculator or online calculator, find the values of tan(45.4°) and tan(33.5°), then substitute them into the formula. The final result will give you the displacement length of the light ray after passing through the material.