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A student focussed the flame of a candle...

A student focussed the flame of a candle on a screen with the help of a convex lens. He noted the positions of candle, lens and screen on the scale as given below:
Position of candle = 14.0 cm, Position of convex lens = 50.0 cm, Position of screen = 86.0 cm
(i) Find the focal length of the lens.
(ii) If under the given condition, height of the flame is 1.5 cm, what would be the height of image obtained on the screen?
(iii) If he displaces the candle to 32.0 cm, where will the image be formed and what will be its nature? Give reason for your answer.
(iv) After this if he further displaces the candle towards the lens, what will be the nature of the image formed and where will it be?
(v) Draw a ray diagram to show the formation of image in the above mentioned case.
[Hints. (i) u = (50-14) cm = 36 cm, v = (86 - 50) cm = 36 cm.
Thus the object is at 2f. Therefore f = 18cm
(ii) Height will be same, i.e., 1.5 cm
(iii) u = 50-32 = 18 cm. Thus, object will be at focus. Therefore, image will be at infinity and is real, inverted and enlarged.
(iv) Object will come in between focus and optical centre.
Image will be virtual, erect and enlarged and formed on the same side of lens as the object.

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