A 2 cm high object is placed at a distance of 20 cm from a concave
formed at 40 cm from the mirror. Calculate the focal length of the mirror.
Answers
Answer:
Given:
The given question states the distance of the object from the mirror denoted as u is 20 cm and is to be taken as negative due to sign convention.
The distance of the image from the mirror denoted as v is 40 cm and is also to be taken negative.
The height of the object is 2cm.
Solution:
We can apply the mirror formula,
\frac{1}{v}+\frac{1}{u}=\frac{1}{f}
v
1
+
u
1
=
f
1
\frac{1}{-40}+\frac{1}{-20}=\frac{1}{f}
−40
1
+
−20
1
=
f
1
\frac{-1-2}{40}=\frac{1}{f}
40
−1−2
=
f
1
f=-\frac{40}{3}f=−
3
40
f = - 13.33 cm
Magnification is calculated by the formula given below,
m=-\frac{v}{u}m=−
u
v
m=\frac{\text {Height of image}}{\text {Height of object}}m=
Height of object
Height of image
-\frac{v}{u}=\frac{\text {Height of image}}{\text {Height of object}}−
u
v
=
Height of object
Height of image
-\left(\frac{-40}{-20}\right)=\frac{\text {Height of image}}{2}−(
−20
−40
)=
2
Height of image
Height of image = -4 cm"
Explanation:
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