GO Figure 33-61 depicts a simplistic optical fiber: a plastic core (n1 = 1.58) is surrounded by a plastic sheath (n2 = 1.53). A light ray is incident on one end of the fiber at angle θ. The ray is to undergo total internal reflection at point A, where it encounters the core-sheath boundary. (Thus there is no loss of light through that boundary.) What is the maximum value of θ that allows total internal reflection at A?
Figure 33-61 Problem 65.
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- 53 SSM www ILW In Fig. 33-53, a ray is incident on one face of a triangular glass prism in air. The angle of incidence e is chosen so that the emerging ray also makes the same angle e with the nor- mal to the other face. Show that the index of refraction n of the glass prism is given by sin ( + 6) sin o where o is the vertex angle of the prism and is the deviation angle, the total angle through which the beam is turned in passing through the prism. (Under these conditions the deviation angle u has the smallest possible value, which is called the angle of mini- mum deviation.) Figure 33-53 Problems 53 and 64.arrow_forward106 In Fig. 33-78, where n, = 1.70, n2 = 1.50, and nz = 1.30, light re- %3D fracts from material 1 into material 2. If it is incident at point A at the critical angle for the interface be- tween materials 2 and 3, what are (a) the angle of refraction at point B and (b) the initial angle 0? If, in- stead, light is incident at B at the critical angle for the interface between materials 2 and 3, what are (c) the angle of refraction at point A and (d) the initial angle e? If, instead of all that, light is incident at point A at Brewster's angle for the interface between materials 2 and 3, what are (e) the angle of refraction at point B and (f) the initial angle 6? Figure 33-78 Problem 106.arrow_forwardIn the figure, light from ray A refracts from material 1 (n1 = 1.60) into a thin layer of material 2 (n2 = 1.80), crosses that layer, and is then incident at the critical angle on the interface between materials 2 and 3 (n3 = 1.3). (a) What is the value of incident angle θA? (b) If θA is decreased, does part of the light refract into material 3? Light from ray B refracts from material 1 into the thin layer, crosses that layer, and is then incident at the critical angle on the interface between materials 2 and 3. (c) What is the value of incident angle θB? (d) If θB is decreased, does part of the light refract into material 3?arrow_forward
- *67 O In the ray diagram of Fig. 33-63, where the angles are not drawn to scale, the ray is incident at the critical angle on the inter- face between materials 2 and 3. Angle o = 60.0°, and two of the in- dexes of refraction are n = 1.70 and n2 = 1.60. Find (a) index of refraction n3 and (b) angle 0. (c) If øi decreased, does light refract into material 3? Figure 33-63 Problem 67.arrow_forward(a) In the figure, light from ray A refracts from material 1 into a thin layer of material 2, crosses that layer, and is then incident at the critical angle on the interface between materials 2 and 3. (i) What is the value of incident angle θA? Draw a sketch of the situation. (ii) If θA is decreased, does part of the light refract into material 3? (b) Light from ray B refracts from material 1 into the thin layer, crosses that layer, and is then incident at the critical angle on the interface between materials 2 and 3. (iii) What is the value of incident angle θB? Draw a sketch of the situation. (iv) If θB is decreased, does part of the light refract into material 3? Answer: 54.3°, yes, 51.1°, noarrow_forwardIn the figure, light initially in material 1 refracts into material 2, crosses that material, and is then incident at the critical angle on the interface between materials 2 and 3. The indices of refraction are n1 = 1.54, n2 = 1.36, n3 = 1.16. (a) What is angle θ? (b) If θ is increased, is there refraction of light into material 3?arrow_forward
- In the figure, light from ray A refracts from material 1 (n₁ = 1.73) into a thin layer of material 2 (n2 = 1.80), crosses that layer, and is then incident at the critical angle on the interface between materials 2 and 3 (n3 = 1.40). (a) What is the value of incident angle BA? (b) If 8A is decreased, does part of the light refract into material 3? Light from ray B refracts from material 1 into the thin layer, crosses that layer, and is then incident at the critical angle on the interface between materials 2 and 3. (c) What is the value of incident angle Og? (d) If Og is decreased, does part of the light refract into material 3? OB I ng no 121arrow_forward46 In Fig. 33-47a, a light ray in an underlying material is incident at angle on a boundary with water, and some of the light refracts into the water. There are two choices of underlying ma- terial. For each, the angle of refraction 02 versus the incident angle is given in Fig. 33-47b. The horizontal axis scale is set by 0₁s = 90°. Without calculation, determine whether the index of refraction of (a) material 1 and (b) material 2 is greater or less than the index of water (n = 1.33). What is the index of refrac- tion of (c) material 1 and (d) material 2? Water (a) 0₂ 90° 45° 0° 1 (b) Figure 33-47 Problem 46. -0₁ 01sarrow_forwardA ray is traveling in material a when it reaches an interface with material b, where n < na. If the critical angle for total internal reflection at this interface is erit = 30.0°, what is the ratio of the speed of light in material a to the speed of light in material b, va/v6? O 1.6 O 0.50 O 0.25 O 1.0 O o o oarrow_forward
- The index of refraction of the core of a piece of fiber optic cable is 1.72. If the index of the surrounding cladding is 1.41, what is the critical angle for total internal reflection for a light ray in the core incident on the core-cladding interface? a 55.1° b 44.0⁰ c 49.6° d 60.6°arrow_forwardA light ray is incident normal to one face of a triangular block and strikes point P on the other side. The block is made of material with index of refraction of 1.71. The block is immersed in oil, having index of refraction of 1.10. What is the maximum angle y for which total internal reflection occurs at P? P O Not possible to have total reflection at P. O 30° O 60° O 50° O 40° O 45°arrow_forwardConsider scenarios A to F in which a ray of light traveling in material 1 is incident onto the interface with material 2. (Figure 1) Material 1 (n1) Material 2 (n2) A air (1.00) water (1.33) В water (1.33) air (1.00) diamond (2.42) air (1.00) D air (1.00) quartz (1.46) E benzene (1.50) water (1.33) F diamond (2.42) water (1.33) Part A For which of these scenarios is total internal reflection possible? List all correct answers in alphabetical order. For example, if scenarios A and E are correct, enter AE. • View Available Hint(s)arrow_forward
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