19. An object 4 cm in height, is placed at
15 cm 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.
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Answer:
The "u" distance of the image is given as -15 cm while the focal length of the object is given is -10 CM.
Now putting these values in the lens formula we can get the distance of the image formed
\frac{1}{v} + \frac{1}{u} = \frac{1}{f} \rightarrow \frac{1}{v} = \frac{1}{15} - \frac{1}{10}
v
1
+
u
1
=
f
1
→
v
1
=
15
1
−
10
1
⇒ v = -30 cm
After knowing the distance of object to be placed let us see the formula for magnification given by -\frac{v}{u}−
u
v
.
On applying the value we get,
m =\frac{h'}{h}
h
h
′
= - \frac{-30}{-15}−
−15
−30
⇒ h’ = -30 \times \frac{4}{15}−30×
15
4
= -8cm
for the purpose of getting an image that is sharp it should be placed at 30 cm.
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