Question

Object of height 4 cm is placed at a distance of 30 cm from the optical centre of a convex lens of focal length 20cm draw a ray diagram to find the position and size of the image formed mark optical Centre O and principal focus f on a diagram also find the approximate ratio of size of the image to size of the object

Answer 1

u = -30 cm
f = 20cm
h= 4 cm.

1/v- 1/u = 1/f
1/v= 1/20-1/30
= (3-2)/ 60
1/v = 1/60
v= 60 cm.

m=v/u = h'/h
60/-30= h' / 4
-2 = h'/4
h' = -8

ratio = - 2:1

Answer 2

$\bf\huge\boxed{\boxed{\bf\huge\:See\:Attached\:Image}}}$

$\bf\huge\frac{1}{v} - \frac{1}{u} = \frac{1}{f}$

$\bf\huge\frac{1}{v} = \frac{1}{f} + \frac{1}{u}$

$\bf\huge\frac{1}{v} = \frac{1}{20} - \frac{1}{30}$

$\bf\huge\frac{1}{v} = \frac{3-2}{60}$

$\bf\huge\frac{1}{v} = \frac{1}{60}$

$\bf\huge\frac{h1}{h} = \frac{v}{u}$

$\bf\huge\frac{h1}{4} = \frac{60}{-30}$

$\bf\huge\texttt h1 = -8cm$

$\bf\huge\texttt Ratio = \frac{Height\:of\:Image}{Height\:of\:Object}$

$\bf\huge\frac{-8}{4} = \frac{-2}{1}$

$\bf\hugeRatio = -2 : 1$

$\bf\huge m = -2 : 1$

$\bf\huge\boxed{\boxed{\bf\huge\:Image=\:Real\:Inverted\:and\:Enlarged}}}$