Example 4

A glass of unknown index of refraction is shaped in the form of an isosceles prism with an apex angle of 25°. In the laboratory, with the help of a laser beam and a prism table, the minimum angle of deviation for this prism is measured carefully to be 15.8°. What is the refractive index of this glass material?

Solution: Given that Ōm = 15.8° and A = 25°, we use Equation 3-4 to calculate the refractive index.



(Comparing this value with refractive indexes given in Table 3-1, the unknown glass is probably flint glass.)

2. Dispersion of light.Table 3-1 lists indexes of refraction for various substances independent of the wavelength of the light. In fact, the refractive index is slightly wavelength dependent. For example, the index of refraction for flint glass is about 1% higher for blue light than for red light. The variation of refractive index n with wavelength λ is called dispersion. Figure 3-12a shows a normal dispersion curve of nλ versus λ for different types of optical glass. Figure 3-12b shows the separation of the individual colors in white light—400 nm to 700 nm— after passing through a prism. Note that nλ decreases from short to long wavelengths, thus causing the red light to be less deviated than the blue light as it passes through a prism. This type of dispersion that accounts for the colors seen in a rainbow, the “prism” there being the individual raindrops.