An object of height is placed at a distance of from the optical centre 'O' of a convex lens of focal length . Add diagramMark optical centre ' ' and principal focus 'F' on the diagram. The approximate ratio of size of the image to the size of the object is ____ and the size of image is ____cm.

Question

An object of height is placed at a distance of from the optical centre 'O' of a convex lens of focal length . Add diagramMark optical centre ' ' and principal focus 'F' on the diagram. The approximate ratio of size of the image to the size of the object is and the size of image is cm.

Accepted Answer

Concept- The approximate ratio of size of the image to the size of the object is 2: 1. To get the value of image distance, use the lens formula. Draw the entire device as a ray diagram after that. Lastly, determine the picture's magnification and size, which are correlated with the distance between the image and the object.
Formula Used:
Lens equation is

And the magnification,

Given that an object of height

is placed at a distance of

from the optical centre 'O' of a convex
lens of focal length

.

By sign convention since image is kept at the left of the lens

Using lens equation we get,

We put the values of the known quantities

Thus the image is formed at the right side of the lens at a distance of

from the lens.
Now we represent the above problem in a ray diagram
Question Image

Here the optical centre '

' and principal focus '

' are marked on the diagram
Now we know that,

Putting the values we get,

The negative sign here shows that the image is inverted and hence real.
Thus the approximate ratio of size of the image to the size of the object is 2: 1
Again

So, the size of image is

.
Hence, the correct answer is 2:1 and 8 cm.

An object of height is placed at a distance of from the optical centre 'O' of a convex lens of focal length . Add diagramMark optical centre ' ' and principal focus 'F' on the diagram. The approximate ratio of size of the image to the size of the object is and the size of image is cm.

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