The focal length of a lens is inversely proportional to the quantity (n 1), wher
ID: 1570880 • 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 = 1.575 for red light and nv = 1.613 for violet light. Now, suppose a white object is placed 23.50 cm in front of a lens made from this type of glass. If the red light reflected from this object produces a sharp image 52.00 cm from the lens, where will the violet image be found?
Explanation / Answer
The focal length of a red light is given by,
1 / d0 + 1 / di,red = 1 / fred
1 / (23.5 cm) + 1 / (52 cm) = 1 / fred
1 / fred = 0.061784 cm
fred = 16.1 cm
We know that, the focal lengths are inversely proportional to (n - 1).
Then, we have
fviolet / fred = (nr - 1) / (nv - 1)
fviolet = (16.1 cm) [(1.575 - 1) / (1.613 - 1)]
fviolet = (16.1 cm) (0.938)
fviolet = 15.1 cm
Therefore, the violet image distance will be given as -
using a len's formula, we have
1 / d0 + 1 / di,violet = 1 / fviolet
1 / di,violet = 1 / (15.1 cm) - 1 / (23.5 cm)
1 / di,violet = 0.023672 cm
di,violet = 42.2 cm
The violet light is in focus [(52 - 42.2) cm = 9.8 cm] before the red light.