#### 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 *f *= ?

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`

Is there an error in this question or solution?

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.