CBSE Class 10 Science 2017 Delhi Term II Set 1 Paper

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Question : 16
Total: 36
An object 4‌cm in height, is placed at 15‌cm in front of a concave mirror of focal length 10 cm. At what distance from the mirror should a screen be placed to obtain a sharp image of the object. Calculate the height of the image.
Solution:  
Given : u=−15‌cm,f=−10‌cm,ho=4‌cm
Using the mirror formula
‌
1
v
+‌
1
u
‌
=‌
1
f

‌
1
v
−‌
1
15
‌
=‌
−1
10

‌
1
v
‌
=‌
−1
10
+‌
1
15

‌
1
v
‌
=‌
−15+10
150
=‌
−5
150

v‌=−30‌cm
Thus, to obtain a sharp image of the object, the screen should be placed in front of the mirror at a distance of 30‌cm.
Now,
m=‌
−v
u
=‌
‌ height of image ‌
‌ height of object ‌

m=−(‌
−30
−15
)
⇒m
=−2

−2=‌
hi
4
⇒hi
=−8‌cm

∴ Height of the image is 8‌cm. (inverted)
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