The focal length of a lens is inversely proportional to the quantity ( n 1), whe

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= 1.607 in violet light. Now, suppose a white object is placed 24.00 cm in front of a lens made from this type of glass.

If the red light reflected from this object produces a sharp image 56.00 cm from the lens, where will the violet image be found?

Explanation / Answer

focal length f = k/(n-1)

for red

1/s + 1/s' = 1/f = (nr-1)/k

1/24 + 1/56 = (1.575-1)/k

k = 9.66

for violet

1/s + 1/s' = 1/f = (nv-1)/k

1/24 + 1/s' = (1.607-1)/9.66

s' = 47.23 cm

the sharp image of violet is formed at 47.23 cm

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