An object is placed at a distance of 5cm from a concave mirror who se focal length is 5cm
a. where is the object placed
b. find the image distance
c. write the properties of the image formed
d. draw relevant ray diagrams
Answers
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.
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