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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

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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=2.81`cm 

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

  Is there an error in this question or solution?

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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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