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Question

An object is placed 30 mm in front of a lens. The distance between the image and object is 120 mm. Which among the following can be correct for the given condition?
  1. Focal Length of the lens is 22.5 mm
  2. The lens is diverging in nature
  3. The lens is converging in nature
  4. The focal length of the lens is 37.5 mm


Solution

The correct options are
A Focal Length of the lens is 22.5 mm
C The lens is converging in nature
D The focal length of the lens is 37.5 mm
Given: Object distance, u=30 mm, (object is placed on the left side of the mirror.
Let image distance  be v and focal length be f
Here two cases arise:
Case I - Image and object are on different side of the lens.
Case II - Image and object are on the same side of the lens.
Focal length will change for both cases as image distance changes.
Case I - Image and object are on different side of the lens.
As per sign conventions,
u=30 mmv=12030=90 mm
Putting the values in lens formula
1f1v1u
1f190130
1f190 + 130
1f1+390
f904=22.5 mm
Case II - Image and object are on the same side of the lens.
As per sign conventions,
u=30 mmv=(120+30)=150 mm
Putting the values in lens formula
1f1v1u
1f1150130
1f1150 + 130
1f1+5150
f1504=37.5 mm
In both cases positive sign of focal length suggests that its a converging (convex) lens

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