an object 5cm in hight is placed in front of concave mirror and the distance from principal axis is 10cm and focal length 20cm find the nature and magnification of the image
Answers
Answer:
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Explanation:
Given: An object of 5cm tall is placed at a distance of 10cm from a concave mirror of radius of curvature 30cm
To find: the nature, position and size of the image and draw the ray diagram to represent the above case.
Solution:
According to the given criteria,
Let height of the image be h
i
and
Height of the object, h
o
=5cm
Object distance, u=−10cm
Radius of curvature, R=−30cm
We know, focal length, f=
2
R
=
2
30
=−15cm
Now applying mirror formula, we get
f
1
=
v
1
+
u
1
⟹
v
1
=
f
1
−
u
1
⟹
v
1
=
−15
1
−
−10
1
⟹
v
1
=
150
−10+15
=
150
5
⟹v=30cm
Position of the image is behind the mirror at the distance of 30 cm
Magnification, m=−
u
v
=
h
o
h
i
⟹−
−10
30
=
5
h
i
⟹h
i
=3×5=15cm
Nature of the image formed: virtual, erect (as magnification is positive) and enlarged.
Ray diagram is as shown in above figure.