A student focussed the image of a candle flame on a white screen
using a convex lens. He noted down the position of the candle
screen and the lens as under
Position of candle = 12.0 cm
Position of convex lens = 50.0 cm
Position of the screen = 88.0 cm
(i) What is the focal length of the convex lens?
(ii) Where will the image be formed if he shifts the candle towards
the lens at a position of 31.0 cm?
(iii) What will be the nature of the image formed if he further shifts
the candle towards the lens?
(iv) Draw a ray diagram to show the formation of the image in case
(iii) as said above
Answers
(i) object distance u = position of convex lens - position of candle
U = -(50 -12) = -38 cm
image distance v = position of screen -position of convex lens
V-88-50 cm
v- 38 cm
Applying the lens formula:
On calculating focal length will be f-19 cm
(ii) When the candle is shifted towards the lens at a position of 31.0 cm:
Object distance u--(50-31)
U = -19 cm
Applying the lens formula
Therefore, v is infinity
(iii). If the candle is further shifted towards the lens, then the nature of the image formed will be virtual, erect and magnified
Answer:
( i ) . Object distance u = 50 - 26 = 24 cm
Image distance v = 74 - 50 = 24 cm .
Since object distance is equal to image distance.
2 f = 24
= > f = 12 cm
So , focal length of object is 12 cm.
( ii ) . u = 50 - 38 = 12 cm
It's mean candle is at focus.
= > Image will form at infinity.
( ii ) Refer to attachment for ray diagram.
