Problem 1:

Pfund’s method is a technique used for measuring the index of refraction of liquids and solids.  To use the method, you must pick a solid substance which is transparent to visible light or a liquid substance with an index of refraction less than that of its container.  Pfund’s method allows you to measure the index of refraction of a substance to two decimal places.

If light is incident normally on a transparent plate of thickness h with a back surface that is painted white, then the light transmitted through the top surface of the plate will scatter into all directions upon hitting the back surface.  The scattered light will again encounter the top surface, and if it makes an angle q < q_c for total internal reflection with the normal to this surface, it will most likely by transmitted back into the air.  However, if q < q_c, the light will be reflected. The reflected light will then illuminate the back surface.  On the back surface we observe a dark circle of radius r surrounded by a bright region.  The radius of the dark circle is determined by the index of refraction of transparent material.  We have

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Use Pfund’s method to determine the index of refraction of a glass plate and a plastic plate at 633 nm.  All materials needed are found in the optics lab.  Submit a picture of your experimental setup, (use the CCD camera), a description of your experimental procedure, your data analysis, and your results

Problem 2:

If we use Pfund’s method and a liquid target in a container with a transparent bottom of thickness h and index of refraction n_container, we also observe a dark circle with radius r.  The bottom surface of the container must be painted white to scatter the light.  For the liquid in the container we have

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Use Pfund’s method to determine the index of refraction of water and isopropyl alcohol (91%) at 633 nm.  All materials needed are found in the optics lab.  Submit a picture of your experimental setup, (use the CCD camera), a description of your experimental procedure, your data analysis, and your results.

Problem 3:

Mirrors for the HeNe laser wavelength 632.8 nm are constructed from multiple layers of ZnS and ThF₂.  The refractive indices are 2.5 and 1.5, respectively.  The substrate is glass with n = 1.5.  What is the minimum number of layers to produce a reflectance of greater than 99.5%.  Assume normal incidence.