Question

a pinhole camera forms an image of size 10cm .the objectbis 5m tall and 20m away from the pinhole .find the length of the pinhole

Answer 1

Correct Question -

A pinhole camera forms an image of size 10 cm.

The object is 5m tall and 20m away from the pinhole .

Find the length of the pinhole.

Solution -

In the above Question , the following information is given -

A pinhole camera forms an image of size 10 cm.

The object is 5m tall and 20m away from the pinhole .

To find -

We have to find the length of the pinhole .

Now we know that -

Magnification

=> [ Height Of Image ] / [ Height Of Object ]

=> [ 10 cm ] / [ 500 cm ]

=> [ 1 / 50 ]

Magnification is also equal to -

=> [ v / u ]

We know that value of u as 20m or 2000 cm

So ,

[ v / 2000 ] = [ 1 / 50 ]

=> v = [ 2000 / 50 ]

=> V = 40 cm

Here, length of the pinhole refers to the focal length of the pinhole .

So,

[ 1 / f ]

=> [ 1 / u ] + [ 1 / v ]

=> [ 1 / 2000 ] + [ 1 / 40 ]

=> [ 51 / 2000 ]

Hence ,

Focal length

=> ( 2000 / 51 ) cm

=> ( 20 / 51) m

=> 0.392 metres approx .

=> 39.2 cm approx ... Answer

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