An object is placed at a distance of 20 cm from a concave mirror, producing a real image. When the object is moved to a distance of 40 cm from the mirror, the new image produced is also real. If the distance between these two image positions is 36 cm , the magnitude of the focal length of the mirror is:

Step-by-step solution

Let the focal length of the concave mirror be f = -F (where F > 0 ). Using the mirror formula 1 v + 1 u = 1 f , we get v = uf u-f . For the first position ( u₁ = -20 cm ): v₁ = (-20)(-F) -20 - (-F) = 20F F - 20 Since the image is real, v₁ For the second position ( u₂ = -40 cm ): v₂ = (-40)(-F) -40 - (-F) = 40F F - 40 Since F The distance between the two image positions is |v₁ - v₂| = 36 cm . Since the object is moved away from the mirror, the real image moves closer to the focus, so |v₁| > |v₂| . |v₁| - |v₂| = 20F