Question

Rohit focused the image of a candle flame on a white screen using a convex lens.<br />
He noted down the position of the candle , screen and lens as under :<br />
Position of candle = 26.0 cm<br />
Position of convex lens = 50.0 cm<br />
Position of screen = 74.0 cm<br />
i) What is the focal length of the convex lens?<br />
ii) Where will the image be formed if he shifts the candle towards the lens at a<br />
position of 38 cm?<br />
iii) Draw a ray diagram to show the formation of the image in case (ii) as said<br />
above?

Answer 1

Position of candle = 26cm
Position of convex lens = 50cm
Position of screen = 74cm

In attachment , I saw position of all the given things
form here, it is clear that,
(i) object (candle ) distance from lens , u = 50cm - 26cm = 24cm
image (on screen) distance from lens ,v = 74cm - 50cm = 24cm
Here , v = u
it means object place at centre of curvature of lens
so, u = 2f , f is focal length
f = u/2 = 24/2 = 12cm

(ii) position of candle = 38cm
so, object (candle ) distance from convex lens = position of convex lens - position of candle = 50cm - 38cm = 12cm
∴ u = -12cm and focal length f = 12cm
Now, use formula,
1/f = 1/v - 1/u
1/12 = 1/v -1/-12
⇒ v = ∞ , hence image is formed at infinity .

(iii) shown in figure

Answer 2

Position of candle = 26cm

Position of convex lens = 50cm

Position of screen = 74cm

In attachment , I saw position of all the given things

form here, it is clear that,

(i) object (candle ) distance from lens , u = 50cm - 26cm = 24cm

image (on screen) distance from lens ,v = 74cm - 50cm = 24cm

Here , v = u

it means object place at centre of curvature of lens

so, u = 2f , f is focal length

f = u/2 = 24/2 = 12cm

(ii) position of candle = 38cm

so, object (candle ) distance from convex lens = position of convex lens - position of candle = 50cm - 38cm = 12cm

∴ u = -12cm and focal length f = 12cm

Now, use formula,

1/f = 1/v - 1/u

1/12 = 1/v -1/-12

⇒ v = ∞ , hence image is formed at infinity .