Chapter 9 · Light - Reflection and Refraction

NCERT Class 10 Science Chapter 9 Intext Questions (Page 158)

All 3 questions of NCERT Class 10 Science Chapter 9 Intext Questions (Page 158) — Light - Reflection and Refraction — in the book's order, each with its answer and a step-by-step solution.

1. Q1
   Define $1$ dioptre ​of ​power ​of a ​lens.
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   One dioptre is the power of a lens of focal length 1 m, so $1\text{D}=1{\text{m}}^{-1}$.

   One dioptre is the power of a lens whose focal length is $1$ metre. Since the power of a lens is the reciprocal of its focal length, $P=1/f$ with $f$ in metres, putting $P=1$ gives $f=1$ m. The unit is denoted by D, and being the reciprocal of a length it satisfies $1$ D $=1$ m${}^{-1}$.

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2. Q2
   A ​convex lens forms a real and inverted image of ​a needle ​at a distance of $50$ cm ​from it. ​Where is the needle placed in front of the convex lens if the ​image is ​equal to the size of the object? Also, find the ​power of the lens.
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   The needle is 50 cm in front of the lens ($u=-50\text{cm}$), and the power is $P=+4\text{D}$.

   The needle is placed $50$ cm in front of the convex lens ($u=-50$ cm), at twice the focal length; the image forms at twice the focal length on the other side, which is why it comes out the same size as the object. The focal length is $f=+25$ cm $=+0.25$ m, so the power of the lens is $P=1/f=+4$ D.

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3. Q3
   Find the ​power of ​a ​concave lens ​of ​focal length $2$ m.
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   The power is $P=-0.5\text{D}$; the minus sign shows that the concave lens is diverging.

   The power of the lens is $-0.5$ D. The lens is concave, so its focal length is negative, $f=-2$ m; since the power is the reciprocal of the focal length in metres, $P=1/(-2)=-0.5$ D. The minus sign is part of the answer — it is what identifies the lens as a diverging one.

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