Question

a student focused the image of a candle flame on a white screen by placing the flame at various distances from a convex lens . he noted his observations as : it is in the image

Answer 1

Lens formula :

1/f = 1/v - 1/u

Convex lens :

u = -ve

v = +ve ( mostly )

f = +ve

Find the focal length by trial and error :

(i)

v = 20

u = 60

1/f = 1/v - 1/u

= > 1/f = 1/20 - ( -1/60 )

= > 1/f = 1/20 + 1/60

= > 1/f = ( 3 + 1 ) / 60

= > 1/f = 4/60

= > 1/f = 1/15

= > f = 15

(ii)

v = 40

u = 24

1/f = 1/v - 1/u

= > 1/f = 1/40 - ( -1/24 )

= > 1/f = 1/40 + 1/24

= > 1/f = ( 3 + 5 ) / 120

= > 1/f = 8/120

= > 1/f = 1/15

= > f = 15

(iii)

v = 30

u = 30

1/f = 1/v - 1/u

= > 1/f = 1/30 - ( -1/30 )

= > 1/f = 1/30 + 1/30

= > 1/f = ( 1 + 1 ) / 30

= > 1/f = 2/30

= > 1/f = 1/15

= > f = 15

(iv)

v = 24

u = 40

1/f = 1/v - 1/u

= > 1/f = 1/24 - ( -1/40 )

= > 1/f = 1/24 + 1/40

= > 1/f = ( 5 + 3 ) / 120

= > 1/f = 8/120

= > 1/f = 1/15

= > f = 15

(v)

u = 15

v = 70

1/f = 1/v - 1/u

= > 1/f = 1/70 - ( -1/15 )

= > 1/f = 1/70 + 1/15

= > 1/f = ( 3 + 14 ) / 210

= > 1/f = 17/210

= > f= 210/17

Thus all cases reveal that f = 15 .

However last one shows f = 210/17 .

So last observation is incorrect.

The focal length of the lens is 15 cm.