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=1.572 for red light and nv= 1.615 in violet light. Now, suppose a white object is placed 21.50 cm in front of a lens made from this type of glass.

If the red light reflected from this object produces a sharp image 54.00 cm from the lens, where will the violet image be found?

Find: di, viol (in cm)

Answer 1

f_r = C / ( 1/1.572 -1 )

= C / 0.572

f_v = C / ( 1/1.615 -1 )

= C / 0.615

f_v / f_r = 0.572 / 0.615

= 0.93

f_r = i x o / ( i + o )

= 21.5 x 54 / ( 21.5 + 54 )

f_r = 15.377 cm

f_v = 0.93 x 15.377

f_v = 14.301 cm

i = o x f / ( o - f )

= 21.5 x 14.301 / ( 21.5 - 14.301 )

i = 42.511 cm