An object of height 4.0 cm is placed at a distance of 30 cm from the optical centre‘O’ of a convex lens of focal length 20 cm. Draw a ray diagram to find the position and size of the image formed. Mark optical centre ‘O’ and principal focus ‘F’ on the diagram. Also find the approximate ratio of size of the image to the size of the object.
Given: Height of the object = AB = 4 cm
Object’s distance from optical centre = u = -30 cm (distance in the direction opposite to the incident ray is taken to be negative)
Focal length of the convex lens = F = 20 cm
Let the distance of the image formed from the optical centre be v and the height of it be A’B’.
The expression to determine the distance of the image formed is given by,
As mentioned in the question the object is placed at 30 cm from the optical centre O of a convex lens with a focal length of 20 cm, therefore substituting the value of u. We get,
We obtain the value of v, which is equal to 60 cm.
Now the magnification of the image is defined as,
Therefore, ratio of the height of image to the height of the object is 2:1
Hence, the ray diagram will look like this,
Ray Diagram
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