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An object of height 4 cm is kept at a distance of 30 cm from the pole of a diverging mirror. If the focal length of the mirror is 10 cm, the height of the image formed is

  1. +3.0 cm
  2. +2.5 cm
  3. +1.0 cm
  4. +0.75 cm

Reflection of Light

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Answer

+1.0 cm

Reason — Given, convex mirror as diverging mirror.

focal length (f) = 10 cm

u = -30 cm

ho = 4 cm

v = ?

Using formula,

1f\dfrac{1}{\text{f}} = 1v\dfrac{1}{\text{v}} + 1u\dfrac{1}{\text{u}}

We get,

110\dfrac{1}{\text{10}} = 1v\dfrac{1}{\text{v}} - 130\dfrac{1}{\text{30}}

1v\dfrac{1}{\text{v}} = 110\dfrac{1}{\text{10}} + 130\dfrac{1}{\text{30}}

1v\dfrac{1}{\text{v}} = 3+130\dfrac{3+1}{\text{30}} = 430\dfrac{4}{\text{30}}

1v\dfrac{1}{\text{v}} = 215\dfrac{2}{\text{15}}

v = 152\dfrac{15}{\text{2}} = 7.5

m = - vu\dfrac{\text{v}}{\text{u}} = hiho\dfrac{\text{h}i}{\text{h}o}

Substituting we get,

-7.5−30\dfrac{7.5}{-30} = hi4\dfrac{\text{h}_i}{4}

height of the image = 7.5×430\dfrac{7.5 \times 4}{30} = +1 cm

Hence, height of the image = +1 cm

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