Ray of laser start from the air and collide with the middle side of some matter > How many total internal reflections done in this matter ??
n ( matter)= 1.48
n (air)= 1.00
The length of matter = 42.0 cm
The width of matter = 3.1 mm
Ray of laser collide by angle =20(degree)
Draw the figure. Next, determine the critical angle. Now start to use a geometrical plot to trace the ray. At each side interaction, determine the angle: below critical or not, determine.
To determine the number of total internal reflections in the matter, we need to consider the conditions for total internal reflection to occur.
When a ray of light travels from a medium with a higher refractive index to a medium with a lower refractive index (in this case, from the matter to the air), total internal reflection can occur if the angle of incidence is greater than the critical angle. The critical angle is the angle at which the angle of refraction becomes 90 degrees (or when the refracted ray travels parallel to the boundary).
In this case:
- The refractive index of the matter (n1) is 1.48.
- The refractive index of air (n2) is 1.00.
- The angle of incidence (θ1) is 20 degrees.
First, we need to calculate the critical angle (θ2) using the formula:
sin(θ2) = n2/n1
Substituting the values:
sin(θ2) = 1.00 / 1.48.
θ2 ≈ 43.72 degrees.
Since the angle of incidence (20 degrees) is less than the critical angle (43.72 degrees), we don't have total internal reflection at the first boundary.
However, total internal reflection can occur on the other side of the matter, where the ray of laser enters the matter again.
To calculate the position of the ray of laser's entry point on the opposite side, we can use trigonometry.
The width of the matter is given as 3.1 mm. The position of entry can be calculated using the formula:
Entry position (d) = width/tan(θ1).
Substituting the values:
d = 0.031 m / tan(20 degrees).
d ≈ 0.090 m.
Now, to calculate the number of reflections, we divide the total length of the matter (42.0 cm) by the distance between each reflection (which can be twice the "entry position" as the ray of laser enters and exits the matter).
Number of reflections = Length of matter / (2 x entry position).
Number of reflections = 0.42 m / (2 x 0.090 m).
Number of reflections ≈ 2.33.
Therefore, there should be approximately 2 total internal reflections within the matter.