हिंदी
Tamil Nadu Board of Secondary EducationSSLC (English Medium) Class 10
पाठ्यपुस्तक उत्तर८४४०
अवधारणा स्पष्टीकरण और वीडियो३०४
पाठ्यक्रम

Lens Formula and Magnification

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Estimated time: 10 minutes
Maharashtra State Board: Class 10

Introduction

The lens formula gives the relationship between the object distance (u), image distance (v), and focal length (f) of a lens:

\[\begin{array}
{cc}1 & 1 \\
\mathbf{v} & \mathbf{u}
\end{array}=\frac{1}{\mathbf{f}}\]

This formula applies to both convex and concave lenses, as long as the sign convention is followed.

Maharashtra State Board: Class 10

Derivation of Lens Formula

Step 1: Consider a Convex Lens

  • Optical center: O
  • Focal length: f
  • Object: AB placed beyond 2F
  • Image: A′B', real, inverted, and smaller

Step 2: Use Similar Triangles

From the image:

  1. Triangles △ABO and △A′B′O\triangle △A′B′O are similar:

    \[\frac{A^{\prime}B^{\prime}}{AB}=\frac{OB^{\prime}}{OB}\]

    (Since corresponding angles are equal)

  2. Triangles △A′B′F and △OCF are similar:

    \[\frac{A^{\prime}B^{\prime}}{OC}=\frac{FB^{\prime}}{OF}\]

Since OC=AB, we get:

\[\begin{aligned}
\frac{A^{\prime}B^{\prime}}{AB}=\frac{FB^{\prime}}{OF}
\end{aligned}\]

Step 3: Equating the Ratios

\[\frac{OB^{\prime}}{OB}=\frac{FB^{\prime}}{OF}\]

Since OB′=v, OB=u, and OF=f, rewriting:

\[\frac{v}{u}=\frac{v-f}{f}\]

Step 4: Apply Sign Conventions

Using the Cartesian Sign Convention:

  • OB = −u (object on the left)
  • OB′ = v (image on the right)
  • OF = f (focal length)

Rewriting:

\[\frac{v-u}{vu}=\frac{1}{f}\]

\[\frac{1}{v}-\frac{1}{u}=\frac{1}{f}\]

Final Result: Lens Formula

\[\frac{1}{v}-\frac{1}{u}=\frac{1}{f}\]

CBSE: Class 10, 12
Maharashtra State Board: Class 10

Formula: Lens Formula

\[\frac {1}{v}\] - \[\frac {1}{u}\] = \[\frac {1}{f}\]

CBSE: Class 10

Formula: Lens Magnification

Magnification (m) = \[\frac{\text{Height of the Image}}{\text{Height of the object}}=\frac{h^{\prime}}{h}\]

Magnification in terms of object and image distances:

Magnification (m ) = \[\frac {h'}{h}\] = \[\frac {v}{u}\]

Related QuestionsVIEW ALL [11]

How are power and focal length of a lens related? You are provided with two lenses of focal length 20 cm and 40 cm respectively. Which lens will you use to obtain more convergent light?

A convex lens of focal length 10 cm is placed at a distance of 60 cm from a screen. How far from the lens should an object be placed so as to obtain a real image on the screen?

Where should an object be placed in front of a convex lens of focal length 0.12 m to obtain a real image of size three times the size of the object, on the screen?

Write the lens formula explaining the meaning of the symbols used.

A lens forms the image of an object placed at a distance of 45 cm from it on a screen placed at a distance 90 cm on the other side of it. Find:

  1. the focal length of lens,
  2. the magnification of the image.

A lens of power +2·5D is kept in contact with another lens of power -2·5D. Draw the path of a ray passing through the lens combination.

The correct lens formula is ______.

A concave lens forms the image of an object kept at a distance 20 cm in front of it, at a distance 10 cm on the side of the object.

  1. What is the nature of the image?
  2. Find the focal length of the lens.
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