A student focused the image of a candle flame on a white screen using a convex lens. He noted down the positions of the candle flame, screen and the lens as given below: Position of the candle flame = 12.0cm; Position of the lens= 50.0 cm; Position of the screen= 88.0 cm; (i)Find the focal length of the convex lens.; (ii)Find the position of the image of the candle flame if it is shifted towards the lens at a position of 31.0 cm.; (iii)State the nature of the image formed if the candle flame is further shifted towards the lens.(All India - 2013)
Answers
Answer:
(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
(iv) The ray diagram will be as follows:
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.
