A ray of light stikes a flat 2 cm thick block of ice (n=1.5) at an angle of 45 degrees. Refracted ray travels through the glass and then is refracted back to air at the opposite side of the block. Find the angles of incident and refraction at each surface.
Snell's law states that:
(sin theda 1/ sin theda 2) = (n2/n1)
sin 45 / sin theda 2 = 1.5/1
arcsin(.707/1.5)= theda 2
=28 degrees
This is the angle of refraction. Would this completely answer the question. What does it mean by "at each surface"? The front and back of the glass? also isn't angle of incidence given as 45 degrees so i don't have to answer that question do i?
i = 38° and r =65°
To solve this problem, you have correctly found the angle of refraction at the first surface using Snell's law. The angle of incidence is indeed given as 45 degrees, so you don't need to calculate it. However, the question asks for the angles of incident and refraction at each surface. This means you need to find the angles of incidence and refraction at both the front and back surfaces of the glass block.
Let's name the angles and surfaces for clarity. Let θ1 be the angle of incidence at the front surface, θ2 be the angle of refraction at the front surface, θ3 be the angle of incidence at the back surface, and θ4 be the angle of refraction at the back surface.
Already, you know that θ1 = 45 degrees and θ2 = 28 degrees (angle of refraction at the front surface).
To find the angles θ3 and θ4, you can use Snell's law again. The incident medium changes from air to glass at the front surface, so the refractive index changes to 1.5 (n2) from the initial index of air which is 1 (n1).
Applying Snell's law at the back surface, you have:
(sin θ3 / sin θ4) = (n2 / n1) = (1.5 / 1)
Since sin θ3 equals sin θ1 (angle of incidence at the front surface), and using the known values:
(sin θ1 / sin θ4) = 1.5
Rearranging the equation:
sin θ4 = sin θ1 / 1.5
Now, substitute the known value of θ1 (45 degrees) into the equation:
sin θ4 = sin 45 / 1.5
Calculating sin 45:
sin 45 ≈ 0.707
Substituting the value of sin 45 into the equation:
sin θ4 = 0.707 / 1.5
Calculating sin θ4:
θ4 ≈ arcsin(0.707 / 1.5)
Using a calculator, you can find that θ4 ≈ 30.257 degrees.
Thus, the angles of incidence and refraction at each surface are:
- Front surface: θ1 = 45 degrees, θ2 = 28 degrees
- Back surface: θ3 = θ1 = 45 degrees, θ4 ≈ 30.257 degrees