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# A Lens Forms a Real Image 3 Cm High of an Object 1 Cm High. If the Separation of Object and Image is 15 Cm, Find the Focal Length of the Lens. - CBSE Class 10 - Science

ConceptReflection of Light Spherical Mirrors

#### Question

A lens forms a real image 3 cm high of an object 1 cm high. If the separation of object and image is 15 cm, find the focal length of the lens.

#### Solution

Given,
Height of image (​h') = - 3 cm (negative because image is real)
Height of ​object = 1 cm
Let us first define the sign convention:
Since the object distance is always negative, let it be -u.
Since the focal length is positive for a convex lens, let it be +f .

Magnification  =h/h=v/u

v/u=-3

(i) Since object distance (u) is always negative, and the ratio v/u here is negative,  v must be positive, i.e., it is on the right side of the lens.

Now, we have object distance + image distance = 15

v+(-u)=15 (using sign convention)

-3u-u=15

-4u=15

u=(-15)/4

Applying the lens formula:

1/f=1/v-1/u

1/f=1/(-3u)-1/u

1/f=(-4)/(3u)

f=(3u)/-4=(3xx-15/4)/4=45/16=2.81cm

Hence, the focal length of the lens is +2.81 cm.

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Solution A Lens Forms a Real Image 3 Cm High of an Object 1 Cm High. If the Separation of Object and Image is 15 Cm, Find the Focal Length of the Lens. Concept: Reflection of Light - Spherical Mirrors.
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