The focal length of a lens is inversely proportional to the quantity (n1), where

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= 1.569 for red light and nv= 1.601 in violet light. Now, suppose a white object is placed 26.50 cm in front of a lens made from this type of glass.

If the red light reflected from this object produces a sharp image 53.00 cm from the lens, where will the violet image be found?

Explanation / Answer

let fr and fv are the focal length of the lens for red and violet colors.

for red light,

u = 26.50 cm

v = 53.00 cm

now use, 1/fr = 1/u + 1/v

1/fr = 1/26.50 + 1/53.00

fr = 17.7 cm

now use Lens makers equation,

1/fr = (nr - 1)*(1/R1 - 1/R2)

1/fv = (nv - 1)*(1/R1 - 1/R2)

(1/fr)/(1/fv) = (nr - 1)/(nv - 1)

fv = fr*(nr - 1)/(nv - 1)

= 17.7*(1.569 - 1)/(1.601 - 1)

= 16.7 cm

noe for violet light

u = 26.50 cm
fv = 16.7 cm
v = ?

use, 1/u + 1/v = 1/fv

1/v = 1/fv - 1/u

1/v = 1/16.7 - 1/26.5

v = 45.1 cm <<<<<<<<-------------------Answer

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