A ray of light traveling in air strikes a flat 2 cm thick block of glass (n=1.50) at an angle of 30° with the normal. Trace the light ray through the glass, and find the angles of incidence and refraction at each surface.
To trace the path of the light ray through the glass and find the angles of incidence and refraction at each surface, you can use Snell's law. Snell's law relates the angle of incidence to the angle of refraction for light passing from one medium to another.
Here are the steps to find the angles of incidence and refraction at each surface:
Step 1: Determine the angle of incidence at the first surface of the glass. In this case, the angle of incidence is given as 30° with respect to the normal.
Step 2: Apply Snell's law to find the angle of refraction at the first surface. Snell's law states that n1*sin(θ1) = n2*sin(θ2), where n1 and n2 are the refractive indices of the initial and final mediums, and θ1 and θ2 are the angles of incidence and refraction, respectively. In this case, n1 is the refractive index of air (approximately 1.00) and n2 is the refractive index of glass (1.50). Plugging in the values, we get: 1.00*sin(30°) = 1.50*sin(θ2). Solving for θ2 gives us: θ2 = arcsin((1.00*sin(30°))/1.50). Evaluating this expression, we find θ2 ≈ 19.47°.
Step 3: The ray of light enters the glass, so the angle of incidence at the second surface is the angle of refraction at the first surface, which is 19.47°.
Step 4: Apply Snell's law again to find the angle of refraction at the second surface. Using the same values as in Step 2 (n1 = 1.50 and n2 = 1.00), we have: 1.50*sin(19.47°) = 1.00*sin(θ2). Solving for θ2 gives us: θ2 = arcsin((1.50*sin(19.47°))/1.00). Evaluating this expression, we find θ2 ≈ 31.62°.
So, the angles of incidence and refraction at each surface are:
First surface:
Angle of incidence = 30°
Angle of refraction = 19.47°
Second surface:
Angle of incidence = 19.47°
Angle of refraction = 31.62°