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Question

For a concave lens of focal length f, the relationship between object and image distances u and v, respectively, from its pole can best be represented by ( u= is the reference line)


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Solution

The correct option is B


Step 1 : Given data

Focal length is f [ f<0, As the lens is concave lens]

Object distance is u u<0

Image distance is v v<0

At reference line u=v

Step 2 : To find its pole best-represented graph

We know the lens formula

1f=1v-1uv=ufu+f

At reference line

u=v

v=(u+f-f)×fu+fv=(u+f-f)u+f.fv=1-fu+f.fv=f-f2u+f [f<0]

If

u=v=f-f2v=f

v=ffor exact idea of curve slope atu=0 will be450 Then, the slope is

dvdu=0+f2u+f2dvduu=0=1

Now, in this graph, the curve, v=f meet at infinity and the tangent from origin is u=v . The tangent should not cut the curve.

Hence, the correct answer is Option B.


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