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

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 n_r = 1.560 for red light and n_v = 1.601 in violet light. Now. suppose a white object is placed 23.00 cm in front of a lens made from this type of glass. If the red light reflected from this object produces a sharp image 56.50 cm from the lens, where will the violet image be found? d_i, void =

Explanation / Answer

Step 1:

Calculate the focal length for red light:

fr = (1/u + 1/v)^-1

fr = (1/23 + 1/56.50)^-1

fr = 16.346 cm

Step 2:

Now calculate the focal length for violet light

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

fv = 16.346*(1.560 - 1)/(1.601 - 1) = 15.231 cm

Step 3:

Now calculate the image distance for violet light:

v = (1/fv - 1/u)^-1

v = (1/15.231 - 1/23)^-1

v = 45.09 cm

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