In Fig. 33-52a, a beam of light in material 1 is incident on a boundary at an angle of θ1 = 30°. The extent of refraction of the light into material 2 depends, in part, on the index of refraction n2 of material 2. Figure 33-52b gives the angle of refraction θ2 versus n2 for a range of possible n2 values. The vertical axis scale is set by θ2a = 20.0° and θ2b = 40.0°. (a) What is the index of refraction of material 1? (b) If the incident angle is changed to 60° and material 2 has n2 = 2.4, then what is angle θ2?
Figure 33-48 Problem 48.
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- 61 Go In Fig. 33-59, 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 indexes of refraction are 1 = 1.60, n2 = 1.40, and n3 = 1.20. (a) What is angle e? (b) If e is in- creased, is there refraction of light into material 3?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_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
- *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_forward6 In Fig. 33-29, unpolarized light is sent into a system of five polarizing sheets. Their polarizing directions, -x measured counterclockwise from the positive direction of the y axis, are the following: sheet 1, 35°; sheet 2, 0°; sheet 3, 0°; sheet 4, 110°; sheet 5, 45°. Sheet 3 is then rotated 180° counter- clockwise about the light ray. During that rotation, at what angles (mea- sured counterclockwise from the y axis) is the transmission of light through the system eliminated? Figure 33-29 Question 6.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_forward
- In Figure (a), a beam of light in material 1 is incident on a boundary at an angle of 28° The extent to which the light is bent due to refraction depends, in part, on the index of refraction n2 of material 2. Figure (b) gives the angle of refraction 02 versus n2 for a range of possible n2 values, from n, = 1.36 to n, = 1.94. What is the speed of light in material 1? 38° 28 28 18 na (a) (b) Number i ! Units m/sarrow_forward1 82 I 9 Figure 33-42 y Xarrow_forward75 SSM In Fig. 33-65, a light ray en- ters a glass slab at point A at incident angle e = 45.0° and then undergoes total internal reflection at point B. Air (The reflection at A is not shown.) What minimum value for the index of refraction of the glass can be in- ferred from this information? Incident ray Glassarrow_forward
- For problem 50(c), find the refracted angle in degrees if the index of refraction of material 3 is 2.00 and the angle of incidence is changed to 53.7 degrees!! (5 sig figs)arrow_forward40 0 In Fig. 33-42, unpolarized light is sent into a system of three polarizing sheets. The angles 61, 62, and 6, of the polariz- ing directions are measured counterclockwise from the positive direction of the y axis (they are not drawn to scale). Angles 0, and 0z are fixed, but angle 6, can be varied. Figure 33-44 gives the intensity of the light emerging from sheet 3 as a function of 6. (The scale of the intensity axis is not indicated.) What percentage of the light's initial intensity is transmitted by the three-sheet system when 0, = 90°? 0° 60° 120° 180° Figure 33-44 Problem 40.arrow_forward*66 o In Fig. 33-62, a light ray in air is incident at angle 6, on a block of transparent plastic with an index of refraction of 1.56. The dimen- sions indicated are H= 2.00 cm and W = 3.00 cm. The light passes through the block to one of its sides and there undergoes reflection (in- side the block) and possibly refraction (out into the air). This is the point of first reflection. The re- flected light then passes through the block to another of its sides-a point of second reflection. If 6 = 40°, on which side is the point of (a) first reflection and (b) second reflection? If there is refraction at the point of (c) first reflection and (d) second reflection, give the angle of refraction; if not, answer "none." If 61 = 70°, on which side is the point of (e) first reflection and (f) second reflection? If there is refrac- tion at the point of (g) first reflection and (h) second reflection, give the angle of refraction; if not, answer “none." н Figure 33-62 Problem 66.arrow_forward
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