A doubleconvex lens with equal 283cm curvature radii is made

A double-convex lens with equal 28.3-cm curvature radii is made from glass with refractive indices n_red = 1.512 and n_violet = 1.547. A point source of white light is located on the lens axis at 79.0 cm from the lens. Over what distance will its visible image be smeared? Follow the sign convention. Express your answer to three significant figures and include the appropriate units.

Solution

For red color :

Raddi of curvature R = 28.3 cm

Index of refraction of red n = 1.512

Focal length for red f =?

From the relation ( 1/f) = (n-1) [(1/R)+(1/R)]

                                 = (1.512-1)(2/R)

                                 = 0.512 (2/28.3)

                                 = 0.03618

                               f = 27.63 cm

Obeject distance u = -79 cm

From the relation (1/v)-(1/u) = (1/f)

                          (1/v) -(1/-79) =(1/27.63)

                           (1/v) = (1/27.63) -(1/79)

                                  = 0.0235

                               v = 42.5 cm

For violet color :

Raddi of curvature R = 28.3 cm

Index of refraction of red n\' = 1.547

Focal length for violet f \' =?

From the relation ( 1/f \') = (n \'-1) [(1/R)+(1/R)]

                                 = (1.547-1)(2/R)

                                 = 0.547 (2/28.3)

                                 = 0.03865

                               f \' = 25.86 cm

Obeject distance u = -79 cm

From the relation (1/v \')-(1/u) = (1/f \')

                          (1/v \') -(1/-79) =(1/25.86)

                           (1/v \') = (1/25.86) -(1/79)

                                  = 0.025999

                               v \' = 38.46 cm

Required separation v - v \'= 4.037 cm