Question

An object 4 cm long and a pencil 9 cm long are placed in front of a pin hole camera such
that their images have the same length. The ratio of the distance of the object from the pin
hole to that of the pencil is:
a) 9:4
b) 4:9
c) 2:3
d) 3:2​

Answer 1

• The ratio of the distance of the object from the pin hole to that of the pencil is 4/5

Given -

• Length of the object = 4 cm
• Length of the pencil = 9 cm

We know that magnification is equals to height of the image to height of the object.

m = Hi/Ho = Di/Do = 1 (Given)

Di /Do = 1

Now for pencil refer to the attached image -

Hi / 9 = Di / x+ y

Hi = 9 Di /x+y     (i)

And for object

9 Di/ x+y = 4 Di/x

so, 9x = 4x + 4y

5x = 4 y

x/y = 4/5

Answer 2

The ratio of the distance of the object from the pin  hole to that of the pencil is x/y = 4/5

Explanation:

Magnification "m" = Hi/Ho = Di/Do

Now for pencil:

Hi/g = Di/x + y

Hi = 9Di/x + y ......(1)

Now for object:

Hi = 4Di/x

Now equating equation (1) and (2)

9Di/x + y = 4Di/x

9x = 4x + 4y

5x = 4y

x/y = 4/5

The ratio of the distance of the object from the pin  hole to that of the pencil is x/y = 4/5

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