Given, a concave lens.
Focal length, f = - 15 cm [f is - ve for a concave lens]
Image distance, v = - 10 cm [image formed is virtual i.e., on same side as the object, so v is - ve]
Now, using the lens formula,
Therefore, object distance, u = −30 cm
In order to make the diagram, let’s use a scale where 5cm = 1cm.
So, as per the new scale,
Focal length, f = -3 cm
Image distance, v = -2 cm
Steps to draw the ray diagram are mentioned below as follows:
(i) Draw a horizontal line which is called the principal axis.
(ii) Now, draw a convex lens keeping principal centre (C) on the principal axis.
(iii) Mark points F (focal length) and B (image distance) on the left side of lens at a distance of 3 cm and 2 cm respectively.
(iv)Draw a dotted line passing through F to any point on the top of the lens, say D.
(v) So, we can draw a line AD parallel to principal axis because any ray of light passing through the focal length of the lens after refraction, passes parallel to the principal axis.
(vi)Draw a line A'B', perpendicular to principal axis from B' representing the height of the image.
(vii) Draw a line CA' backwards, so that it meets the line from D at A.
(viii) Now, draw a line AB, perpendicular to the principal axis at B from point A in the downward direction.
(ix) AB is the position of object. On measuring distance BC, it will be found to be equal to 6 cm.
Thus, the object is placed at a distance of 6 cm × 5 = 30 cm from the lens (as per the original scale).
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