15. Critical angle of glass and water combination, θ = 62.45°
16. Critical angle for the interface between Mystery A and glass, θ = 37.93°
Note; The question is incomplete. The complete question is as follows:
Medium Air Water Glass Mystery A Mystery B Table-2 Speed (m/s) 1.00 C 0.75 c 0.67 0.41 c 0.71 c n 1.00 1.33 1.50 Index of Refraction n of a given medium is defined as the ratio of speed of light in vacuum, c to the speed of light in a medium, v. n = c/v
Table-4: Incident Angle (degrees) Reflected Angle Refracted angle (degrees) (degrees) % Intensity of reflected ray 0 10 20 30 40 50 N/A N/A N/A 30 40 50 0 11.3 22.7 34.2 46.3 59.5 N/A N/A N/A 0.67 1.22 3.08 % Intensity of refracted ray 100 100 100 99.33 98.78 96.92
When rays travel from a denser medium to a less dense medium, we can define a critical angle of incidence θ such that refracted angle θ₂ = 90°. Applying Snell's law: Critical angle θ = sin-1(n₂/n₁).
When the angle of incidence is greater than the critical angle, 100% of the light intensity is reflected. This is called total internal reflection because all the light is reflected.
15. Calculate the critical angle of glass and water combination. Show your calculation.
16. What is the critical angle for the interface between Mystery A and glass?
Explanation:
15. Applying Snell's law; Critical angle θ = sin-1(n₂/n₁).
where n₂,refractive index of water = 1.33, n₁, refractive index of glass = 1.50 since glass is denser than water
θ = sin-1(1.33/1.50)
θ = 62.45°
Critical angle of glass and water combination, θ = 62.45°
16. Refractive index of mystery A , n = c/v
where v = 0.41 c
therefore, n = c / 0.41 c = 2.44
Critical angle for the interface between Mystery A and glass, θ = sin-1(n₂/n₁).
where n₂,refractive index of glass = 1.50, n₁, refractive index of mystery A = 2.44 since mystery A is denser than glass as seen from its refractive index
θ = sin-1(1.50/2.44)
θ = 37.93°
Critical angle for the interface between Mystery A and glass, θ = 37.93°
