Ray Optics and Optical Instruments Part 1

Let v be the position of image, h be the height of image and ho be the height of object.
Given, hi=ho
Since, magnification, m=hi∕ho=hi∕h . . . (i)
By using lens formula,
1∕f=1∕v−1∕u⇒1∕v=1∕f+1∕u
‌‌v=‌

fu

u+f

‌‌m=‌

v

u

=‌

f

f+u

Now, from Eq. (i), m can be ±1.
For, m=+1=‌

f

−10+f

. . . (ii)
For m=−1=‌

f

−20+f

. . . (iii)
On dividing Eq. (iii) by Eq. (ii), we get
−1=‌

−10+f

−20+f

⇒‌‌20−f=−10+f⇒30=2f
⇒‌‌f=15cm