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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 below,
Position of candle = $12 cm$

Position of convex lens = $50 cm$

Position of the screen = $88 cm$

The image will be formed at ____, if he shifts the candle towards the lens at a position of $32 cm .$

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Detailed Solution

The image will be formed at infinity, if he shifts the candle towards the lens at a position of

31 cm .

Given,

u

is the distance of candle from the lens

\Rightarrow (50 - 12) = 38 cm

According to sign convention,

u = - 38 cm

Now,

v

is the distance of image from the lens

\Rightarrow (88 - 50) = 38 cm

As per sign convention,

v = 38 cm

Using lens formula,

\frac{1}{f} = \frac{1}{v} - \frac{1}{u}

\frac{1}{f} = \frac{1}{38} + \frac{1}{38}

f = \frac{38}{2} = 19 cm

If the student shifts the candle towards the lens at a position of

32 cm

.
Object distance, u

= (50 - 32) \Rightarrow 19 cm

.
Thus,the candle lies at the focus.
Hence, the image will be formed at infinity.

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