Question

How can you find out focal length of convex lens?

Answer 1

Answer:

Explanation:

Focal length is distance over which the parallel rays either converge or diverge. For convex lens the focal length is positive.

now let,

h= height of the object

h’= height of the object projected in an image

G and C = focal points

f= focal distance

u= Distance between the object and the focal point

O= Centre of the lens

v= Distance between the centre of the lens and image plane

Assumptions

Lens is very thin

Optical axis is perpendicular to image plane

Proving  is true.

Proof

In ΔAHO,  

tan alpha = h / u

In ΔEDO,  

tan alpha = h' / v

∴   tan alpha = h /u = h' / v

v / u = h' / h

—– (1)

In ΔBOC,  

tan beta  = h / f

In ΔEDC,  

tan beta = h' / v- f

tan beta = h/f = h' / v-f

∴  v- f / f = h' h

—— (2)

Equating equations (1) and (2),

v / u = v-f / f

v/u = v / 1-f

Dividing both sides by v,

1/u  = 1/f - 1/ v

Hence the formula is proved.

1 / f = 1 /u + 1/v