Question

An object is 15.2 cm to the left of a lens with a focal length of 10.2 cm. A second lens of focal length 11.8 cm is 39.27 cm to the right of the first lens. The height of the object of is 2.1 cm. What is the location of the final image with respect to the second lens? What is the height of the image?

Answer 1

as from the given

   p₁ = 14.6 cm

   f₁ = 10.2 cm

   the thin lens equation gives the position of theimage formed by the first lens as

   q₁ = p₁ f₁ /(p₁ - f₁)

       = (14.6 cm) (10.2) /(14.6 cm - 10.2 cm)

       =33.84cm

   this image serves as an object for the second lens with an object distance of

   p₂ = 10.2 cm - q₁

       = -23.84 cm (a virtual object)

   if the image formed by this lens is at the position O₁ the image distance will be

   q₂ = - (10.2 cm + p₁)

        = - (10.2 cm + 14.6cm)

        = - 24.28cm

   so from the thin lens equation we get the focallength of the second lens as

   f₂ =  p₂q₂ / (p₂ + q₂)

       = -12.02cm

thanks