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 {\cm}

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

4 {\cm}

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

20 {\cm}

. The distance of the object from the lens is

15 {\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 {\cm}

from the lens.

Given :

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

We know that,

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

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

∴

Image distance,

v=-60 {\cm}

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

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

h_2=\;{v}/{u} × h_1=\;{-60}/{-15} × 4=+16 {\cm} .

The size of the image is

16 {\cm}

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