CBSE Class 10 Science 2017 · Paper 31(B)/C · Question 23

Four points of the New Cartesian sign convention (pole $P$ as origin, principal axis as the $x$-axis): (1) The object is always placed to the left of the mirror, so that light from the object falls on the mirror from the left. (2) All distances parallel to the principal axis are measured from the pole. (3) Distances measured to the right of the pole, in the direction of the incident light, are positive; those measured to the left are negative. (4) Distances measured perpendicular to the principal axis are positive above it and negative below it. Radius of curvature $+30$ cm: the centre of curvature lies behind the mirror, so the mirror is a convex mirror; its focal length is $f=\frac{R}{2}=+15$ cm. Screen: with $u=-30$ cm and $f=-20$ cm, $\frac{1}{v}=\frac{1}{f}-\frac{1}{u}=-\frac{1}{20}+\frac{1}{30}=-\frac{1}{60}$, so $v=-60$ cm. The screen should be placed $60$ cm from the mirror, in front of it, on the same side as the object; the image there is real, inverted and twice the size of the object.