Object AB is placed on the axis of a concave mirror of focal length 10cm. End A of the object is at 30cm from the mirror. Find the length of the image
a. if length of object is 5cm.
b. if length of object is 1 mm.

Explanation

a. For a point A, u=-30cm, f=-10cm
Using `1/v+1/u=1/f, 1/(v^('))-1/(30)=-1/(10)rArrv=-15cm`
Similarly, for point B, u=-35 cm, f=-10cm
Using `1/v+1/u=1/f, ` we get
`v^(') =-14cm`
Now, size of image
`|A^(')B^(')|=|v-v^(')|=|(-15)-(-14)|=1cm`
b. Here, `u=-30cm, f=-10cm`
Using `1/v+1/u=1/f,`
`1/v+1/((-30))=1/((-10))rArr v=-15cm`
Now,`(dv)/(du)=-((-15)^(2))/((-30)^(2))rArr |dv| =((15)^(2))/((30)^(2))|du|`
`rArr |dv|=((225)/(900))(10^(-3))=2.5xx10^(-4)m`
So the length of the image is `2.5xx10^(-4)m`