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# An Object of Height 4 Cm is Placed at a Distance of 15 Cm in Front of a Concave Lens of Power, −10 Dioptres. Find the Size of the Image. - CBSE Class 10 - Science

ConceptRefraction at Spherical Surfaces and by Lenses Power of a Lens

#### Question

An object of height 4 cm is placed at a distance of 15 cm in front of a concave lens of power, −10 dioptres. Find the size of the image.

#### Solution

Object distance u = -15 cm
Height of object h  = 4 cm
Power of the lens p = -10 dioptres
Height of image h' = ?
Image distance v = ?
Focal length of the lens = ?

We know that:

p=1/f

f=1/p

⇒f=1/-10

⇒ f=-0.1m =-10 cm

From the lens formula, we have:

1/v-1/u=1/f

1/v-1/-15=1/-10

1/v+1/15=-1/10

1/v=-1/15-1/10

1/v=(-2-3)/30

1/v=-5/30

1/v=-1/6

v=-6 cm

Thus, the image will be formed at a distance of 6 cm and in front of the mirror.
Now, magnification m  =v/u=(h')/h

or (-6)/(-15)=(h')/4

h'=(6x4)/15

h'=24/15

∴h'=1.6 cm

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Solution An Object of Height 4 Cm is Placed at a Distance of 15 Cm in Front of a Concave Lens of Power, −10 Dioptres. Find the Size of the Image. Concept: Refraction at Spherical Surfaces and by Lenses - Power of a Lens.
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