an object 2 cm high is placed at right angles to the principle axis of a mirror of focal length 25 cm such that an erect image 6 cm high is formed by it. then the type of mirror and position of object is?
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Answers
Answer:
Given that,
Distance u=−10cm
Height h=2.5cm
Radius of curvature R=30cm
We know that,
−f=
2
R
−f=
2
30
f=−15cm
Now, using mirror’s formula
f
1
=
v
1
+
u
1
−
15
1
=
v
1
−
10
1
v
1
=−
15
1
+
10
1
v=30cm
Now, the magnification is
m=
u
−v
m=
10
30
m=3
We know that,
m=
h
h
′
3=
2.5
h
′
h
′
=7.5cm
Hence, the size of the image is 7.5 cm
Explanation:
Question : An object 2 cm high is placed at right angles to the principle axis of a mirror of focal length 25 cm such that an erect image 6 cm high is formed by it. Then determine the type of mirror and position of object .
Answer :
The mirror is Concave and the object is at a distance of 50/3cm from the pole.
Given :
object size h0 = 2cm
image size h1 = 6cm
f=25cm
Let v be the image distance and u be the object distance
To find :
the type of mirror and position of object
Solution :
Concave mirror m > 1
m=3
-v/u=3
=> -v =3u
Lens formula :
1/v + 1/u = 1/f
=> -1/3u + 1/u = 1/f
=>2/3u = 1/f
=> f= 34/2
u= (-25 × 2)/3
=-50/3
THEREFORE THE POSITION OF THE OBJECT IS 50/3 cm FROM THE POLE.
AND, as the image is erect,magnified and virtual, therefore the type of mirror is CONCAVE MIRROR.
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