a convex lens forms a real image of a point object at a distance of 50 cm from convex lens. a concave lens is placed 10 cm behind convex lens on image side. on placing a plane mirror on the image side and facing the concave lens it is observed that final image now coincides with the object itself. find focal length of concave lens.

my attempt: v= +50cm for convex lens as real image is formed on opposite side to object.

unable to proceed further


closed as off-topic by ACuriousMind, Kyle Kanos, Martin, John Rennie, Qmechanic May 26 '15 at 7:43

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The image of each individual optical device forms the (pseudo)object for the next optical device in the light path. You must make adjustments for the position difference of each device, and be sure to keep account of positive and negative values of object/image distances.

As a starter for you, the object distance for the concave lens will be be -40 cm.

  • $\begingroup$ can you tell the reason why it is true $\endgroup$ – user184271 Mar 6 '18 at 14:00
  • $\begingroup$ Do you mean: 1) you calculate each element in order using the previous (possible) image position as the effective object positions, or 2) the object distance ....will be -40 cm? $\endgroup$ – Bill N Mar 6 '18 at 19:31
  • $\begingroup$ The first one in my opinion $\endgroup$ – user184271 Mar 6 '18 at 20:51
  • $\begingroup$ Thin lenses and mirrors can be approximated as linear elements whose refractive properties are independent of their placement. Their effects on light are expressed, individually, in terms of where they would focus light if an object is a certain distance from them. This behavior is a characteristic of the lense/mirror and, to first order, is not based on circumstances. So mathematically we "play the game" of finding where the first lense would produce an image, then treat that LOCATION as the object location for the next element. It works because of the approximate linearity of the lenses. $\endgroup$ – Bill N Mar 7 '18 at 18:20
  • $\begingroup$ It works in first order, but if the distances between lenses/mirrors gets to be the same order of magnitude as the curvature of the surfaces, higher order effects and abberations appear. Also, light entering from near the edges of the lenses is not focused well, either, in spherical lenses. Refractive dispersion can be a problem also, if high quality imaging at multiple wavelengths (white light) is required. $\endgroup$ – Bill N Mar 7 '18 at 18:24

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