Question

a stick of length f/2 is placed on principal axis of a concave mirror of focal length f such that the image of one end coincides. then the length of its image will be

Answer 1

look at the attachment

• Length of rod given by f/2

Radius of the culvature=2f

Now

• Object distance =PC-AB=2f-f/2=4f-f/2=-3f/2

Applying Mirror formula

`\\ \rm\longmapsto (1)/(v)-(1)/(u)=(1)/(f)`

`\\ \rm\longmapsto (1)/(v)=(1)/(u)+(1)/(f)`

`\\ \rm\longmapsto (1)/(v)=(1)/(-3f/2)+(-1)/(f)`

`\\ \rm\longmapsto (1)/(v)=-(2)/(3f)-(1)/(f)`

`\\ \rm\longmapsto (1)/(v)=(2-3)/(3f)`

`\\ \rm\longmapsto (1)/(v)=(-1)/(3f)`

`\\ \rm\longmapsto v=-3f`

• v is iage distance

Now

`\\ \rm\longmapsto m=(h')/(h)=-(v)/(u)=`

`\\ \rm\longmapsto m=(f)/(f/2)`

`\\ \rm\longmapsto m=2`