Question

An object is placed at a distance of 100 cm from each of the above lenses A and B. Calculate

1. image distance, and
2. magnification, in each of the two cases.

Answer 1

Object distance (u) = -100 cm (sign convention)
For lens A:
Image distance (v) = ?

Using the lens formula, we get:  

`1/v-1/u=1/f` 

⇒`1/v-1/-100=1/50` 

⇒`1/v+1/100=1/50` 

⇒`1/v=1/50-1/100` 

⇒`1/v=2-1/100`  

⇒`1/v=1/100`  

∴ v = 100 cm.  

∴Magnification =` v/u=100/-100=-1`  

For lens B:
Image distance (v₂) = ? 

Using the lens formula, we get: 

`1/v-1/u=1/f`  

⇒`1/v-1/-100=1/-25` 

⇒`1/v+1/100=1/-25` 

⇒`1/v=-1/25-1/100` 

⇒`1/v=(-4-1)/100` 

⇒`1/v=(-5)/100` 

∴v = -20cm 

Negative sign shows that the image formed is virtual.

∴ Magnification = `v/u=(-20)/-100=0.2.`