Physics-
General
Easy

Question

An object is placed 20 cm in front of a plano–convex lens of focal length 15 cm. The plane surface of the lens is silvered. The image will be formed at a distance

  1. 60 cm to the left of the lens    
  2. 12 cm to the right of the lens    
  3. 60 cm to the right of the lens    
  4. 12 cm to the left of the lens    

The correct answer is: 12 cm to the right of the lens


    Focal length F of equivalent mirror is given by
    fraction numerator 1 over denominator F end fraction equals fraction numerator 2 over denominator f subscript e end subscript end fraction plus fraction numerator 1 over denominator f subscript m end subscript end fraction equals fraction numerator 2 over denominator 15 end fraction plus fraction numerator 1 over denominator infinity end fraction or F equals fraction numerator 15 over denominator 2 end fraction cm
    The equivalent mirror will concave mirror of focal length fraction numerator 15 over denominator 2 end fraction cm.
    Now for a spherical mirror,
    fraction numerator 1 over denominator v end fraction plus fraction numerator 1 over denominator u end fraction equals fraction numerator 1 over denominator F end fraction Þ fraction numerator 1 over denominator v end fraction plus fraction numerator 1 over denominator negative 20 end fraction equals fraction numerator negative 2 over denominator 15 end fraction
    Þ fraction numerator 1 over denominator v end fraction equals fraction numerator negative 2 over denominator 15 end fraction plus fraction numerator 1 over denominator 20 end fraction equals fraction numerator negative 8 plus 3 over denominator 60 end fraction equals negative fraction numerator 5 over denominator 60 end fraction equals negative fraction numerator 1 over denominator 12 end fraction
    v = –12 cm

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