A screen is placed 90cm from an object. The image of the object on the screen is formed by a convex lens at two different locations separated by 20cm. Determine the focal length of the lens.

Question

anonymous · Answer

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In first case :

u=-x    
v=90-x

By the lens formula ,we will get

    1/90-x     +     1/x     =    1/f


In second case

u = -(20+x)
v = 70-x

This time
  
    1/70-x       +      1/20+x    = 1/f

Equating the two

  1/70-x        +    1/20+x         =        1/90-x       +    1/x

This looks like a quadratic equation but is infact a linear equation and quite easy to solve.  Find x and put it back in any of the above two equations and find f.