a convex lens of focal length 6cm forms a real image of the same size as the object. the distance between the object and image will be
(a)9cm (b)18cm (c)12cm (d)24cm
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A convex lens of focal length 6cm is held 4cm from a newspaper which has print 0.5cm high. By calculation , determine the size and nature of the image produced.
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f=6cm
u=−4cm
h
1
=0.5cm
Lens formula :
v
1
−
u
1
=
f
1
v
1
−
−4
1
=
6
1
v
1
=
6
1
−
4
1
=
12
2−3
v=−12cm
m=
u
v
=
h
1
h
2
−4
−12
=
0.5
h
2
h
2
=1.5cm
Image is 1.5cm high , virtual , erect and magnified.
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Given: A convex lens of focal length 6 cm forms a real image of the same size as the object.
To find: Distance between the object and image
Explanation: Since it is a convex lens, the focal length of the lens will be positive in nature.
Let focal length be denoted as f.
f= +6 cm
It is given that the image is same size as that of object, therefore magnification will be 1.
m= v/u ( magnification formula for lens)
=> 1 = v/u
=> v = u
It shows that object distance is same as image distance.
This is possible when the object is at the position 2F where 2F is the position which is at a distance of twice the length of the focal length.
Object distance= 2* focal length (f)
= 2*6
= 12 cm
Since image distance is same as object distance,
Image distance is also equal to 12 cm.
Distance between image and object
= 12+12 cm
= 24 cm
Therefore, the distance between image and object will be option (d) 24 cm.