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CBSE Class 10 Science Question 12 of 31

Light - Reflection and Refraction — Question 12

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Question 12

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

Answer

Given,

f = +15 cm

u = -10 cm

v = ?

According to the mirror formula,

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

Substituting the values we get,

1v+1−10=115⇒1v=110+115⇒1v=3+230⇒1v=530⇒1v=16⇒v=6 cm\dfrac{1}{v} + \dfrac{1}{-10} = \dfrac{1}{15} \\[1em] \Rightarrow \dfrac{1}{v} = \dfrac{1}{ 10} + \dfrac{1}{15} \\[1em] \Rightarrow \dfrac{1}{v} = \dfrac{3+2}{30} \\[1em] \Rightarrow \dfrac{1}{v} = \dfrac{5}{30} \\[1em] \Rightarrow \dfrac{1}{v} = \dfrac{1}{6} \\[1em] \Rightarrow v = 6\text{ cm}

Therefore, image is formed 6 cm behind the mirror. Image is virtual and erect.