One half of a convex lens of focal length 10 ...

CBSE Class 10 Science 2015 Term II Outside Delhi Set 1

Question : 23 of 36

Marks: +1, -0

One half of a convex lens of focal length 10 cm is covered with a black paper. Can such a lens produce an image of a complete object placed at a distance of

30\text{ cm}

from the lens? Draw a ray diagram to justify your answer. A

4\text{ cm}

tall object is placed perpendicular to the principal axis of a convex lens of focal length

20\text{ cm}

. The distance of the object from the lens is

15\text{ cm}

. Find the nature, position and size of the image.

Solution:

Yes, it can produce an image of a complete object placed at a distance of

30\text{ cm}

from the lens.

Given :

h_1=4\text{ cm},\; f=+20\text{ cm},\; u=-15\text{ cm}

We know that,

\;\frac{1}{f}= \;\frac{1}{v}- \;\frac{1}{u}

\;\frac{1}{v}= \;\frac{1}{f}+ \;\frac{1}{u}= \;\frac{1}{20} \;\; \;\frac{1}{15}= \;\frac{34}{60}= \;\frac{1}{60}

\therefore

Image distance,

v=-60\text{ cm}

Image will be virtual, erect and placed in the direction of the object.

Now, Magnification,

m=\;\frac{h_2}{h_1}=\;\frac{v}{u}

h_2=\;\frac{v}{u} \times h_1=\;\frac{-60}{-15} \times 4=+16\text{ cm} .

The size of the image is

16\text{ cm}

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