Question

a student has to project a three times magnified image of a candle flame on a wall .name the type of the lens (converging or diverging) required for the purpose. if the candle flame is at a distance of 6 metre from the wall ,find the focal length of the lens.

Answer 1

Given:
Converging lens or Convex lens should be used by the user to project the image of candle on the wall as he wants it to be three times magnified.

Reason:
In Convex lens, when object is placed between F and C , the image will be formed beyond C .
Nature of Image :
--> magnified, real and inverted.

2) hi=3ho
Image distance= object distance + 6
v=6+u
we know that magnification=m=v/u
m=v/u
-3=v/u[since image is magnifed three times ]
-3=6+u/u
-3u=6+u
4u=-6
u=-6/4
u=-1.5 m
v=6-(-1.5)
v=7.5m
by using lens formula,
1/f =1/v-1/u
1/7.5 +1/1.5=1/f
10/75+10/15=1/f
10+50/ 75=1/f
∴ f=75/60=1.25m
Thus, Focal length of a given convex lens is 1.25m

Answer 2

sol:

Here m= -3

as image is formed on the wall balance must be converging


m= v/u

putting m=3 in this equation

v= 3u
as candle flame is at distance of 6m from the wall
u+v= 6
as we know that v= 3
putting the value of v in eqn.........

u+3u =6
4u = 6

u= 6/4
u= 1.5

as we know that v=3u
putting the value of u in this equation

v= 3×1.5
= 4.5m

using proper sign convention
here,
u= -1.5m,

v= +4.5m

as we know that the mirror formula,

1/f = 1/v + 1/u

putting the value of v, and u in this equation

=1/4.5 - 1/-1.5

=1 +3/4.5
= 4/ 4.5

f=4.5/4
=1.125m