PhysicsAn object 1 m tall is placed on the principal axis of a convex lens and its 40 cm tall image is formed on the screen placed at a distance of 70 cm from the object. The focal length of the lens.

An object 1 m tall is placed on the principal axis of a convex lens and its 40 cm tall image is formed on the screen placed at a distance of 70 cm from the object. The focal length of the lens.


  1. A
    +15 cm
  2. B
    +14.3 cm
  3. C
    +17 cm
  4. D
    -16 cm 

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    Solution:

    An object 1 m tall is placed on the principal axis of a convex lens and its 40 cm tall image is formed on the screen placed at a distance of 70 cm from the object. The Focal length of the lens, f=+14.3 cm
    Given,
    Height of the object, h=1 m
    Height of the real image formed on the screen, h'=-40 cm
    Distance from object to screen, u+v=70 cm
    m=h'h=vu
    vu=-40cm1m
    =-40 cm100 cm
    =-0.4
    v=-0.4u or v=0.4u
    u+v=u+0.4u
    =1.4u
    =70 cm
     u=701.4
    =50 cm
    And hence,
    v=70-u
    =70-50
    =20 cm
    As per sign convention, u is -ve and v is +ve, i.e, u=-50 cm and v=+20 cm
    1f=1v-1u
    =1+20-1-50
    =120+150
    =5+2100
    1f=7100
    f=1007
    =+14.3 cm.
     
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