Math Problem Statement
Determine the critical angle for quartz, using the Index of Refraction Table in Question 3.
[3 marks]
The critical angle for sapphire is 34.4°. For each angle of incidence, determine if it would result in total internal reflection in a sapphire by writing Yes/No. [4 marks]
a) 23.7° _____________________ c) 53.4° _____________________ b) 34.7° _____________________ d) 31.5° _____________________
- A diver shines a flashlight toward the air-water boundary at an angle of 35° to the normal. At what angle does the flashlight beam leave the water? Assume that the index of refraction for the water is 1.33. [3 marks]
Solution
Question 1: Determine the critical angle for quartz
To determine the critical angle () for quartz, we use Snell's Law:
At the critical angle, is 90° (the angle of refraction), so:
For total internal reflection to occur, light must travel from a medium with a higher refractive index () to one with a lower refractive index (). Assuming is the refractive index of quartz and is the refractive index of air (approximately 1):
Given:
- for quartz ≈ 1.54 (common value for quartz)
Question 2: Total Internal Reflection in Sapphire
Given the critical angle for sapphire is 34.4°, we need to determine if the following angles of incidence result in total internal reflection (TIR) in sapphire. TIR occurs when the angle of incidence is greater than the critical angle.
a) 23.7°
No
b) 34.7°
Yes
c) 53.4°
Yes
d) 31.5°
No
Question 3: Refraction of Light from Water to Air
Using Snell's Law to determine the angle at which the flashlight beam leaves the water:
Given:
- (water) = 1.33
- (air) ≈ 1
- Angle of incidence in water () = 35°
Since must be less than or equal to 1, there's an error. We need to reassess our calculation as follows:
Thus, the angle at which the flashlight beam leaves the water is approximately 49.8°.
Do you want more details or have any questions?
Here are some related questions you might be interested in:
- What is the general principle behind Snell's Law?
- How do you derive the formula for the critical angle?
- What factors affect the critical angle of a material?
- How does total internal reflection apply to optical fibers?
- What are some practical applications of total internal reflection?
- How does the index of refraction vary with wavelength?
- Can the critical angle change if the surrounding medium changes?
- How does refraction differ from reflection?
Tip: The critical angle is a unique property of the material and the medium into which the light is transitioning. It only occurs when light moves from a medium with a higher index of refraction to one with a lower index of refraction.
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Math Problem Analysis
Mathematical Concepts
Optics
Snell's Law
Index of Refraction
Formulas
Snell's Law: n₁ sin θ₁ = n₂ sin θ₂
Theorems
-
Suitable Grade Level
University
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