The focal length of a lens is inversely proportional to the quantity (n1), where
ID: 1348171 • Letter: T
Question
The focal length of a lens is inversely proportional to the quantity (n1), 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= 1.608 in violet light. Now, suppose a white object is placed 21.00 cm in front of a lens made from this type of glass.If the red light reflected from this object produces a sharp image 57.00 cm from the lens, where will the violet image be found?
Answer in cm
Explanation / Answer
focal length f = k/(n-1)
for red
1/s + 1/s' = 1/f = (nr-1)/k
1/21 + 1/57 = (1.575-1)/k
k = 8.82
for violet
1/s + 1/s' = 1/f = (nv-1)/k
1/21 + 1/s' = (1.608-1)/8.82
s' = 46.9 cm
the sharp image of violet is formed at 46.9 cm