Turn in your answers to the following problems below. As always, make sure to show all of your work.

1. The so-called “hydrogen alpha (Ha) line” is a specific wavelength of red light caused by excited atomic hydrogen. It is frequently used when studying the Sun. The wavelength of Ha is 656.3 nm, or 656.3*10^{-9} m. The speed of light in vacuum is 3*10^{8} m/s. What is the frequency ( in units of cycles per second, or 1/s) of Ha in vacuum?

2. Light is incident at angle A from a media with n = 1.5 to one with n = 2.0 as shown in the figure. What is the minimum value for A so that there is total internal reflection at point P, which is at the interface between the n = 2 and n = 1 materials?

3. An object of height 5 cm is placed 30 cm in front of spherical concave mirror. If the image is real and 10 cm high, what is the radius of curvature of the mirror?

4. The so-called “lensmakers equation” is shown below. The focal length of the lens (in cm) is f. The constant n is the index of refraction of the glass, relative to the medium around it (which is just the listed value of n unless the lens is submerged in water, or some other liquid). R_{1} and R_{2} are the radii of curvature of the two sides of the lens. The value of R for a side is considered to be positive if that side is convex; otherwise, it is negative. If the lens is flat on one side, the value of R for that side is infinite, and the ratio (1/R) is equal to zero.

Assume the lens is biconvex; that is, that both sides are convex. The radii of curvature are both 20 cm. The coefficient of refraction is 1.40. What is the focal length of the lens, in cm?

5. The index of refraction of a glass varies with the wavelength of the light passing through it. This has important consequences for the design of optical instruments. A type of glass known as “extra-dense flint” has an n = 1.7378 for blue light, and an n of 1.7130 for red light. Calculate the focal length of the lens above, for both red and blue light.

You will find that red and blue light form images at slightly different distances from the lens. This results in a blurred image. The problem is solved by using systems of lenses composed of glasses having different indices of refraction, and different radii of curvature. Such systems are called either achromatic or apochromatic, depending upon the degree of correction. Designing such a system is a non-trivial exercise, and is beyond the scope of this course.

Case Assignment Expectations:

In general, Cases are expected to possess the attributes of precision, clarity, breadth, depth, and critical thinking. Not all of these are relevant to the answer to every problem in the case. When it is relevant, the evidence for each attribute is as follows.

Precision: Numerical answers are calculated correctly, to the correct number of significant figures.

Clarity: The problem is restated in its simplest form. Relevant variables are identified. Formulas are algebraically rearranged, as necessary. All the mathematical steps are shown, in logical order.

Breadth: Where discussion is required, the question is placed in context. Alternatives are considered.

Depth: Where discussion is required, the question is examined in detail. No relevant aspect of the question is omitted.

Critical thinking: The correct analytical approach is selected. Relevant data areidentified and irrelevant data are ignored. When required, the practical importance of the principle or phenomenon is accurately described.