Lens Formula for Concave Lens | Physics Grade XI

Lenses

☰   Related Articles

Refraction Through Prisms

Lens Formula for Concave Lens | Physics Grade XI

Lens Formula for Concave Lens

Lens Formula for Concave Lens

Lens formula for concave lens

Consider a ray AD parallel to principal axis falling onto a concave lens of focal length f and being diverged by passing through E. The ray DE is appeared to be diverged from the focus F, so a virtual line DF is drawn that passes through the principal focus. Another ray AF passes through the optical center Intersecting the virtual ray at H forming a virtual image HI.

From the figure,
     BC = u = object distance
     IC = v = image distance = -v (for virtual image)
     FC = f = focal length = -f (for concave lens)
     DC = AB
 
Since ΔABC ~ ΔHIC
     AB/HI = BC/IC
     AB/HI = u/-v ………… (i)
 
Similarly, in ΔHIC and ΔDCF
     DC/HI = FC/IF
     AB/HI = FC/(FC – IC)
     AB/HI = -f/{-f -(-v)}
     AB/HI = -f/(-f + v) = f/(f-v) ……… (ii)
 
Equating equation (i) and (ii)
         u/-v = f/(f-v)
     uf - uv = -vf
     uf + vf = uv
 
dividing both sides by uvf, we get
     1/f = 1/u + 1/v

You may also like to read:

nephost
Join with us on social media to see our updates on your feed.
facebook logo twitter logo