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An object is placed at a distance of 10 cm from a convex mirror of focal length 15 cm. Find the position of the image formed by the mirror.

Reflection of Light

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Answer

Given,

  • Object distance (u\text u) = -10 cm
  • Focal length of the mirror (f\text f) = 15 cm

Here, negative sign indicates that object is placed in front of the mirror.

By, using the mirror formula,

1f=1v+1u⇒1v=1f−1u⇒1v=115−1(−10)⇒1v=115+110⇒1v=2+330⇒1v=530⇒v=305⇒v=6 cm\dfrac{1}{\text f} = \dfrac{1}{\text v} + \dfrac{1}{\text u} \\[1em] \Rightarrow \dfrac{1}{\text v} = \dfrac{1}{\text f} - \dfrac{1}{\text u} \\[1em] \Rightarrow \dfrac{1}{\text v} = \dfrac{1}{15} - \dfrac{1}{(-10)} \\[1em] \Rightarrow \dfrac{1}{\text v} = \dfrac{1}{15} + \dfrac{1}{10} \\[1em] \Rightarrow \dfrac{1}{\text v} = \dfrac{2 + 3}{30} \\[1em] \Rightarrow \dfrac{1}{\text v} = \dfrac{5}{30} \\[1em] \Rightarrow \text v = \dfrac{30}{5} \\[1em] \Rightarrow \text v = 6 \text { cm}

Hence, the image is formed behind the mirror at a distance of 6 cm from the mirror.

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