Answer :

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

__Ray diagram:__

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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