An image Y is formed of a point object x by a lens whose optic axis is AB as shown in Figure. Draw a ray diagram to locate the lens and its focus. If the image Y of object X is formed by a concave mirror (having the same optic axis AB) instead of lens, draw another ray diagram to locate the mirror and its focus. Write down the steps of construction of the ray diagrams.

Answer

A, C

Explanation

(i) Since Y is below of topic axis, therefore the image is real and inverted. (i) STEPS OF CONSTRUCTION OF DIAGRAM. For convex lens
(1) Join XY. This represents the ray origination from the source and meeting the image Y. Since the ray is undeviated after passing through the lens, therefore O is the optical centre of the lens. Draw `Y_(1)OY_(2)` perpendicular to AB.
(2) Draw a ray from X, parallel to AB. It strikes `Y_(1)OY_(2)` at M. Join MY. It cuts AB at F. This is the focus of the convex lens.
(ii) For concave mirror
As the image is real and inverted, the concave mirror has to be placed towards the left of X. To find the exact position of the concave mirror, we draw a line YY^` perpendicular to AB such that `BY=BY^``
join `Y^`X`and extend the line to meet AB at O. If the concave mirror is placed at O then after reflection at O, this line will meet Y.
To find the radius of curvature of the mirror
join X and Y. Let it cut AB at C. This C should be the centre of curvature of the concave mirror. With OC as radius, draw a part of sphere. This is the concave mirror.
To find the focus of the concave mirror
Draw XM parallel to the principal axis. Join M to Y. Let it cut AD at F. Therefore, F is the focus of concave mirror.