An object of height 2 cm is placed at a distance
20 cm in front of a concave mirror of focal length
12 cm. Find the position, size and nature of the
image.
Ans. 30 cm in front of mirror, 3 cm
Answers
This question could be solved using the mirror equation.
The mirror equation is used in cases when we have the distances, heights, and magnification.
It gives us the relationship between focal length, distance of object and distance of image.
Height of the object = 2cm
Distance (u) = 20 cm
Focal length (f) = 12 cm
Mirror Equation 1/f = 1/v + 1/u
On solving, v = 30 cm
Magnification = -hi/ho = v/u
Size of image hi = -v*ho/u hi = 3cm
Since the object is placed between the focus and center, the image will be real, inverted and magnified.
Answer:
Size of object h
o
=2cm
Size of the object h
i
=?
Focal length f=−12cm
Object distance u=−20cm
Image distance v=?
Using mirror formula
f
1
=
v
1
+
u
1
−12
1
=
v
1
+
−20
1
v
1
=
60
−5+3
v=−30cm
Magnification (M)=
h
o
h
i
=
u
−v
=
−20
30
=−1.5
h
i
=−1.5×2=−3cm
Image will be real, inverted and magnified.