Single Choice

A lens of focal length $$ 12\,cm $$ forms an erect image three times the size of the object. The distance between the object and image is:

A$$ 8\,cm $$
B$$ 16\,cm $$
Correct Answer
C$$ 24\,cm $$
D$$ 36\,cm $$

Solution

Magnification , $$ m = \dfrac{v}{u} $$

$$ 3 = \dfrac{v}{u} $$

$$ \Rightarrow v = 3u $$

Lens formula : $$ \dfrac{1}{v} - \dfrac{1}{u} = \dfrac{1}{f} $$

$$ \dfrac{1}{3u} - \dfrac{1}{u} = \dfrac{1}{12} $$

$$ \dfrac{-2}{3u} = \dfrac{1}{12} $$

$$ \Rightarrow u = -8\,cm $$

$$ v = 3 \times -8 = -24\,cm $$

Distance between object and image $$ = u - v = -8 -(-24) = -8 + 24 = 16\,cm $$

SIMILAR QUESTIONS

Optics

By means of plotting find: The path of ray 2 beyond the converging and diverging lenses (Fig. 5.8 ) if the path of ray 1 and the positions of the lens and of its optical axis $$ O O^{\prime} $$ are all known; the media on both sides of the lenses are identical.

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A Galilean telescope of 10-fold magnification has a length of $$ 45 \mathrm{cm} $$ when adjusted to infinity. Determine: (b) by what distance the ocular should be displaced to adjust the telescope to the distance of $$ 50 \mathrm{m} $$.

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The optical powers of the objective and the ocular of a microscope are equal to 100 and 20 D respectively. The microscope magnification is equal to $$ 50. $$ What will the magnification of the microscope be when the distance between the objective and the ocular is increased by $$ 2.0 \mathrm{cm}? $$

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The distance $$v$$ of real image formed by a convex lens is measured for various object distance $$u$$. A graph is plotted between $$v$$ and $$u$$, which one of the following graphs is correct.

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For a convex lens the distance of the object is taken on $$X-axis$$ and the distance of the image is taken on $$Y-axis$$, the nature of the graph so obtained is

Optics

Find the type of optical instrument and its focal length from the following graph ($$v$$ vs $$u$$)

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(a) Find the nature , position and magnification of the image formed by a convex lens of focal length $$ 0.20\,m $$ if the object is placed at a distance of : (i) $$ 0.50\,m $$ (ii) $$ 0.25\,m $$ (iii) $$ 0.15\,m $$ (b) Which of the above cases represent the use of convex in a film project , in a camera and as a magnifying glass ?

Optics

A magnifying lens has a focal length of $$ 100\,mm $$ . An object whose size is $$ 16\,mm $$ is placed at some distance from the lens so that an image at a distance of $$ 25\,cm $$ in front of the lens. (a) What is the distance between the object and the lens? (b) Where should the object be placed if the image is to form at infinity ?

Optics

Figure. shows variation of magnification $$m$$ (produced by a thin convex lens) and distance $$v$$ of image from pole of the lens. Which of the following statements are correct?

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