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# Homework 7 - Physics 6B, Winter 2013 Posted: 3-5-2013 Adriane Steinacker Due: 3-18-2013 Please note that geometric optics problems must be...

4. A parallel beam of light containing two wavelengths, !1 = 465nm and !2 = 652nm , enters the silicate flint equilateral prism at an angle of incidence of 45o, as shown below.
At what angle does each beam leave the prism (measured with respect to the perpendicular to the face at the point of emergence from the glass)? The corresponding indices of refraction are 1.642 and 1.619. Clearly show the paths if of the beam through the prism and as they emerge into air on the other side.

Homework 7 – Physics 6B, Winter 2013 Adriane Steinacker Posted: 3-5-2013 Due: 3-18-2013 Please note that geometric optics problems must be accompanied by neat figures, preferably on math paper. No points and consideration will be given to sloppy drawings. Please submit only the problems marked in bold font . 1. A violet and a red beam of light, with wavelengths of 400nm and 700nm respectively, simultaneously strike an air-quartz interface with an incidence angle of 60 o . If the indices of refraction for these two wavelengths through quartz are 1.56 and 1.54, (a) what are the angles of refraction for each beam in the quartz slab? (b) Draw a sketch to scale (i.e. the angles must be measured and drawn in by using a protractor). (c) What is the angle between the two beams in the quartz slab? (d) If the two beams propagate in the same direction inside the quartz, for what range of incidence angles on the quartz-air interface, will one beam be totally internally reflected and the other not? (e) What is the angle of refraction for the other beam in this case? (f) For what incidence angle are both beams totally internally reflected? 2. A cubical block is made from two equal-size slabs of materials with different refractive indices, as shown in the figure below. Find the index of the right-hand slab if a light ray is incident on the center of the left-hand slab and then describes the path shown. 3. You lost your key in the pool while diving and now you are searching the bottom of the pool with a narrow beam flashlight. If you are standing right on the edge of the 3m deep pool, you are shining the light from a height of 1.3m as shown in the figure below, and the beam hits the surface of the water 2.5m away from the edge of the pool, where does the beam hit the bottom of the pool?
4 . A parallel beam of light containing two wavelengths, ! 1 = 465 nm and ! 2 = 652 nm , enters the silicate flint equilateral prism at an angle of incidence of 45 o , as shown below. At what angle does each beam leave the prism (measured with respect to the perpendicular to the face at the point of emergence from the glass)? The corresponding indices of refraction are 1.642 and 1.619. Clearly show the paths if of the beam through the prism and as they emerge into air on the other side. 5. A meter stick lies on the bottom of the rectangular tank as shown below. Its zero mark is at the left edge of the tank. You look into the long dimension of the tank at a 45 o angle, with your line of sight just grazing the top edge of the tank. What mark on the meter stick do you see when the tank is (a) empty, (b) half full of water, and (c) full of water? The index of refraction of water is 1.333. 6. The rectangular prism shown in the figure below has an index of refraction of n=1.52. (a) Will the incident beam show undergo total internal reflection? Where and how will it exit the prism? Provide a clear sketch. (b) When the prism is immersed in a liquid, the shown incident beam emerges along the long side of the prism. What is the index of refraction of this liquid? (c) What will happen to the emerging beam if we place the prism into a liquid with a larger index of refraction? (d) If the index of refraction of the liquid is 1.1, what is the angle at which the beam emerged from the prism (measured with respect to a direction normal to the side of the prism at the emergence point)? (e) What would have to be the index of refraction of the liquid in order for the angle asked for at point (d) to be 30 o ?
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4. A parallel beam of light containing two wavelengths, λ1
= 465nm and λ2 = 652nm ,
enters the silicate flint equilateral prism at an angle of
incidence of 45 , as shown below.
At what angle does...

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