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 :
(a) Position of Candle = 12.6 cm
(b) Position of Convex Lens = 51.8 cm
(c) Position of Screen = 91.0 cm
(i) Calculate the focal length of the lens.
(ii) Where will the image be formed if he
shifts the candle towards the lens at a
position of 32.2 cm?
(iii) What will be the nature of the image
formed if he further shifts the candle
towards the lens?
(iv) Dr aw a r a y d i a g r am t o s h ow t h e
formation of the image in case (c) as
said above.

Here, we will measure all distance with respect to the potion of convex lens.

so,

the object distance will be, u = 12.6 cm - 51.8 cm = -39.2 cm

the image distance will be, v =  91.0 cm - 51.8 cm = 39.2 cm

 

(1)

so, the focal length will be calculated using the lens formula

1/f = 1/v - 1/u

or

1/f = (2 / 39.2)

 

thus, the focal length fot he lens is 

f = 19.6 cm

 

(2)

here,

the image distance will be, u = 32.2 cm - 51.8 cm = -19.6 cm

and focal length, f = 19.6 cm

so,

1/v = 1/f + 1/u

or

1/v = 1/19.6 - 1/19.6

so,

v = infinity, the image will be formed at infinity as the object is kept on the point of focus of the lens.

 

(3)

The object is shifted towards the lens, the object distance thus decreases and so we would see a variation in image characteristics. We suggest you look at the ray diagrams in lesson notes for more...

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