The focal length of a lens is inversely proportional to the quantity (n?1), wher
ID: 2254067 • Letter: T
Question
The focal length of a lens is inversely proportional to the quantity (n?1), where n is the index of refraction of the lens material. The value of n, however, depends on the wavelength of the light that passes through the lens. For example, one type of flint glass has an index of refraction of nr= 1.577 for red light and nv= 1.607 in violet light. Now, suppose a white object is placed 21.50cm in front of a lens made from this type of glass.
If the red light reflected from this object produces a sharp image 54.00cm from the lens, where will the violet image be found? (cm)
Explanation / Answer
fr = c / (1.577 -1) = c / .577 given in problem
fv = c / (1.607 - 1) = c / .607
fv / fr = .577 / .607 = .9506
1 / fr = 1 / i + 1 / o
fr = i * o / (i + o) = 21.5 * 54 / (21.5 + 54) = 15.38 cm
fv = .9506 * 15.38 = 14.62 cm
i = o * f / (o - f) = 14.62 * 21.5 / (21.5 - 14.62) = 45.68 cm