In Fig. 33-78, where n1 = l.70, n2 = l .50, and n3 = 1.30, light refracts from material l into material 2. If it is incident at point A at the critical angle for the interface between materials 2 and 3, what are (a) the angle of refraction at point B and (b) the initial angle θ? If, instead, 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 instead angle θ? 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 θ?
Figure 33-78 Problem 106.
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- 106 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 = 1.73) 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_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 = 1.60) 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_forward53 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_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_forward
- 46 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 of light crosses the boundary between some substance with n = 1.61 and air, going from the substance into air. If the angle of incidence is 18◦ what is the angle of refraction? Calculate to 1decimal.arrow_forwardis 90°. 48 In Fig. 33-48a, a light ray in water is incident at angle on a boundary with an underlying material, into which some of the light refracts. There are two choices of underlying material. For each, the angle of refraction 02 versus the incident angle given in Fig. 33-48b. The vertical axis scale is set by 02 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 refraction of (c) material 1 and (d) material 2? Water (a) 0₂ 02s 0° 45° (b) Figure 33-48 Problem 48. 2 90° =arrow_forward
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